for a challenge involving the mathematical operator of division or integer division

Division is the inverse of multiplication on a skew field.

In a skew field division is a binary operator applied to two non-zero elements to produce a single element of the field.

For example in the modular arithmetic Z5

3 / 2 = 4

where / is the division operation.

This is because in Z5

4 * 2 = 3

Most often challenges tagged will operate on the field Q (the rational numbers) or some subset of R (the real numbers).


Integer Division is a generalization of Division onto all rings. Given an element a such that

a = (p * q) + r, r < q

Integer division is the binary operation between a and q that yields p.

a // q = p

where // is the integer division symbol.

On a skew field r will always be the additive identity and thus the result of Integer division and division will always be the same.

Integer division is most common on the ring I (the integers), being the reason it is named Integer division. On I Integer division can be thought of as the floor of the corresponding division on Q.

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