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The Legendre symbol is a number theoretic function (a/p) which is defined to be equal to +/-1 depending on whether a is a quadratic residue modulo p. The definition is ...

Lehmer's totient problem asks if there exist any composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function? No such numbers are known. However, any ...

Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... (OEIS A000027) or to the set of nonnegative integers 0, 1, 2, 3, ... (OEIS ...

A sequence of positive integers 1<=a_1<a_2<a_3<... (1) is a nonaveraging sequence if it contains no three terms which are in an arithmetic progression, i.e., terms such that ...

Let G be a simple graph with nonsingular (0,1) adjacency matrix A. If all the diagonal entries of the matrix inverse A^(-1) are zero and all the off-diagonal entries of ...

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. (1) The ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...