A résolu


Dickson Polynomials
Return the coefficients of nth (n>=0) Dickson polynomial of the 1st kind as follows - 1st row of the output will be the coeffi...

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Measure the hydraulic conductivity with a constant-head permeameter
A constant-head permeameter is a device for measuring the hydraulic conductivity of a soil sample. In this problem the sample i...

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Problème


Multiply real numbers to get the smallest integers
Write a function that takes a vector of real numbers and multiplies them by a factor to produce the integers with the smallest a...

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A résolu


find powers of two
find the unique, non-repeating, powers of 2 that sum to a given non-zero integer, n example: n = 23 result = [1 2 4 16] ...

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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...

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Mesh the icosahedron
Problem statement An icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five...

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Mesh the dodecahedron
Problem statement An dodecahedron is a regular polyhedron with 20 vertices and 12 pentagonal faces. It is also one of the fiv...

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Mesh the pentagon (with the minimum number of triangles)
Problem statement An pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V,...

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Mesh the octahedron
Problem statement An octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five we...

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Mesh the tetrahedron
Problem statement An tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five w...

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Mesh the cube
Problem statement : mesh the cube with quadranglar / squared faces An cube / regular hexahedron is a regular polyhedron with ...

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Problème


Search for seesaw primes
Cody Problem 60958 introduced seesaw numbers. A number is a seesaw number if the next smaller numbers can be placed on a seesa...

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A résolu


Find the Prime Factors and Divisors of a Number
Given a positive integer n, find its prime factors as well as all of its divisors. Example: n=12 has prime factors [2,2,3] and ...

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Mesh the square with triangles
Problem statement An square is a regular polygon with 4 vertices and 4 edges. A triangulated mesh T (stands for triangles he...

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A résolu


Check Euler's characteristic on regular polyhedra
Problem statement Given the number of vertices and the number of faces of a given regular polyhedron, compute the number of its...

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Problème


List numbers that cannot be expressed as the sum of two primes
The Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the...

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A résolu


Monkey and the Peaches
A monkey picked a certain number of peaches on the first day. Each day, the monkey eats half of the remaining peaches plus one ...

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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 : ...

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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...

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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...

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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...

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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...

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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 ...

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List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...

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Determine if LTI system with feedback control is stable
Linear timeiinvariant systems can be represented by the differential equation , where is an matrix, is an vector representing...

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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...

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Problème


Determine whether a number is a seesaw number
Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a giv...

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A résolu


Chek the Delta = 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...

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Problème


List balanced primes
A balanced prime of order is one that equals the average of the primes before it and the primes after it. For example, 79 is ...

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A résolu


Baye's theorem on conditional probability
Let the given probabilities Compute the output probability

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