Elementary number theory

thumb|upright=1.25|The integers arranged on a number line

positive integer that has at least one positive divisor other than 1 or itself

thumb|The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10

shorthand way of determining whether a given number is divisible by a fixed divisor

In mathematics, a half-integer is a number of the form n + \tfrac{1}{2}, where n is an integer. For example, 4\tfrac12,\quad 7/2,\quad -\tfrac{13}{2},\quad 8.5 are all half-integers. The name "half-integer" is perhaps misleading, as each integer n is itself half of the integer 2n. A name such as "integer-plus-half" may be more accurate, but while not literally true, "half integer" is the conventional term. Half-integers occur frequently enough in mathematics and in quantum mechanics that a distinct term is convenient.

Numbers divisible by another number

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product of sums of four squares is a sum of four squares

set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n

how many times a number is divisible by 2