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A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...

A prime p is said to be a Sophie Germain prime if both p and 2p+1 are prime. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, ... (OEIS ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

If a prime number divides a norm but not the bases of the norm, it is itself a norm.

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

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

A number theoretic function is a function whose domain is the set of positive integers.

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

A very large number defined in terms of circle notation by Steinhaus (1983) as .