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The Case of the Missing Prototype – Check the Lab’s Logbook for Suspicious Late-Night Entries
After counting the fingerprints, you turn your attention to the security logbook.It records the entry hours (from 0 to 23) of ev...
4 Tage vor
Gelöst
The Case of the Missing Prototype - Count the Fingerprints Found at the Lab Door to Begin Your Investigation
You arrive at the Innovation Lab where the secret prototype was stolen. The door has been dusted for fingerprints, and a technic...
4 Tage vor
Gelöst
find the nth fibonacci number
The Fibonacci sequence is defined as follows: give n, find the nth fibonacci number
4 Tage vor
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find the nth number (plus)
this problem is the harder version of Problem 61014. The numbers 2 and 7 are called lucky numbers, an integer containing only t...
4 Tage vor
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Find nth number
The numbers 2 and 7 are called lucky numbers, an integer containing only the digits 2 and 7 is also called lucky number. The pro...
4 Tage vor
Gelöst
Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...
7 Tage vor
Gelöst
List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...
7 Tage vor
Gelöst
Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...
7 Tage vor
Gelöst
List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...
7 Tage vor
Gelöst
Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...
7 Tage vor
Gelöst
Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...
7 Tage vor
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Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...
7 Tage vor
Gelöst
Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...
7 Tage vor
Gelöst
List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...
7 Tage vor
Gelöst
The Goldbach Conjecture, Part 2
The <http://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach conjecture> asserts that every even integer greater than 2 can ...
10 Tage vor
Gelöst
Twins in a Window
<http://en.wikipedia.org/wiki/Twin_primes Twin primes> are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a f...
10 Tage vor
Gelöst
Prime factor digits
Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...
10 Tage vor
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Twin Primes
Twin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5,...
10 Tage vor
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Mersenne Primes vs. All Primes
A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. <https://www.mathworks.com/matl...
10 Tage vor
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Mersenne Primes
A Mersenne prime is a prime number of the form M = 2^p - 1, where p is another prime number. For example, 31 is a Mersenne prim...
10 Tage vor
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Circular Primes (based on Project Euler, problem 35)
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. The...
10 Tage vor
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Sophie Germain prime
In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prim...
10 Tage vor
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Find the next prime number
Find the next prime number or numbers for given n. For example: n = 1; out = 2; or n = [5 7]; out = [7 11]; ...
10 Tage vor
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Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...
10 Tage vor
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Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...
10 Tage vor
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LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...
10 Tage vor
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Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...
10 Tage vor
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Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...
10 Tage vor
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Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...
10 Tage vor
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Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...
10 Tage vor
