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The hypothesis that an integer n is prime iff it satisfies the condition that 2^n-2 is divisible by n. Dickson (2005, p. 91) stated that Leibniz believe to have proved that ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...

The Copeland-Erdős constant has decimal expansion C=0.23571113... (OEIS A033308). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, 2, ...

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...

By analogy with the divisor function sigma_1(n), let pi(n)=product_(d|n)d (1) denote the product of the divisors d of n (including n itself). For n=1, 2, ..., the first few ...

Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

A homework problem proposed in Steffi's math class in January 2003 asked students to prove that no ratio of two unequal numbers obtained by permuting all the digits 1, 2, ...