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A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

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; ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

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, ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

A Thâbit ibn Kurrah prime, sometimes called a 321-prime, is a Thâbit ibn Kurrah number (i.e., a number of the form 3·2^n-1 for nonnegative integer n) that is prime. The ...

An Abelian differential is an analytic or meromorphic differential on a compact or closed Riemann surface.

The portion of number theory concerned with expressing an integer as a sum of integers from some given set.

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).