Problem 44319. Write c^3 as sum of two squares a^2+b^2

Mehmet OZC

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write c^3 as sum of two squares a^2+b^2. a and b must be integer and greater than zero.

For example

 5^3 = 2^2 + 11^2
 5^3 = 5^2 + 10^2
 10^3 = 10^2 + 30^2
 10^3 = 18^2 + 26^2

sort output matrix so that each row and first column is in ascending order.

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1144 Solutions

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Last Solution submitted on Feb 04, 2026

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Stephen Cook on 16 Oct 2017

Last test case is wrong. Does not catch 500^3 == 1160^2 + 11120^2 and 500^3 == 2000^2 + 11000^2 .

James on 17 Oct 2017

First case is also wrong: 1^3 = 1^2 + 0^2. The problem doesn't specify positive numbers, so it is a valid solution. (If you *really* want to open a can of worms, a and b don't have to be integers, or even real numbers according to the test suite!)

Mehmet OZC on 18 Oct 2017

You are right James. I have add some sentences to problem definition.

Payam Morsali on 19 Oct 2020

How on earth the leading solution size is 7? can you please provide it also for us ?

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