Problem 53940. Easy Sequences 66: Fractional Part of Sum of Consecutive Powers over a Prime

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given three postive integers, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>e</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, create the function </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>FPSP(x,y,n)</w:t></w:r></w:customXml><w:r><w:t>, defined as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>FPSP(x,e,n)=\\left\\{ \\frac{1}{p_{n}} \\cdot \\sum^{x}_{i=1} i^{e}\\right\\} </w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p_{n}</w:t></w:r></w:customXml><w:r><w:t> is the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>th prime and the symbol </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{\\}</w:t></w:r></w:customXml><w:r><w:t> is the </w:t></w:r><w:hyperlink w:docLocation=\"https://brilliant.org/wiki/factional-part-function/\"><w:r><w:t>fractional part function</w:t></w:r></w:hyperlink><w:r><w:t> of a positive real number, defined as follows: </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> If </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r \\in \\mathbb{R}^{+}</w:t></w:r></w:customXml><w:r><w:t> then </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{r\\}=r-\\lfloor r \\rfloor</w:t></w:r></w:customXml><w:r><w:t>, where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\lfloor r \\rfloor</w:t></w:r></w:customXml><w:r><w:t>, is the 'floor' of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x=10</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>e=2</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=6</w:t></w:r></w:customXml><w:r><w:t>, we have:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\sum^{10}_{i=1} i^{2} = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Therefore, since </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p_6=13</w:t></w:r></w:customXml><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>FPSP(10,2,6)=\\left\\{ \\frac{385}{13} \\right\\} = \\{29.615384561538...\\}=0.61538461538...</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Please round-off the output to four decimal places, so in this case: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>FPSP(10,2,6)=0.6154</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>HINT:</w:t></w:r><w:r><w:t> This is related to the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\"><w:r><w:t>Faulhaber's formula</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

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margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; ">Given three postive integers, x<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">, e<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; "> and n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; ">, create the function <img 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style="width: 85px; height: 18.5px;" width="85" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; ">, defined as follows:</div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 181px; height: 45px;" width="181" height="45"></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; ">Where <img src="data:image/png;base64,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" style="width: 15.5px; height: 20px;" width="15.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; "> is the n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.5px 8px; transform-origin: 77.5px 8px; unicode-bidi: normal; ">th prime and the symbol <img src="data:image/png;base64,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" style="width: 18px; height: 18.5px;" width="18" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; "> is the <a target='_blank' href = "https://brilliant.org/wiki/factional-part-function/">fractional part function</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; "> of a positive real number, defined as follows: </div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; "> If <img src="data:image/png;base64,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" style="width: 46px; height: 19px;" width="46" height="19"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; "> then <img src="data:image/png;base64,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" style="width: 86.5px; height: 18.5px;" width="86.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; ">, where <img src="data:image/png;base64,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" style="width: 23px; height: 18.5px;" width="23" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; ">, is the 'floor' of r<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; ">For example for <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">, <img src="data:image/png;base64,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" style="width: 36px; height: 18px;" width="36" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; ">, we have:</div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 383.5px; height: 45px;" width="383.5" height="45"></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54px 8px; transform-origin: 54px 8px; unicode-bidi: normal; ">Therefore, since <img src="data:image/png;base64,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" style="width: 49px; height: 20px;" width="49" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">:</div><div style="block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> <img 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" style="width: 430.5px; height: 35px;" width="430.5" height="35"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.5px 8px; transform-origin: 210.5px 8px; unicode-bidi: normal; ">Please round-off the output to four decimal places, so in this case: <img src="data:image/png;base64,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" style="width: 152px; height: 18.5px;" width="152" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; ">HINT:<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; "> This is related to the <a target='_blank' href = "https://en.wikipedia.org/wiki/Faulhaber%27s_formula">Faulhaber's formula</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div></div></div>

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Problem 53940. Easy Sequences 66: Fractional Part of Sum of Consecutive Powers over a Prime

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Problem 53940. Easy Sequences 66: Fractional Part of Sum of Consecutive Powers over a Prime

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