Synonyms in mathematics: remainder and residue

The remainder is what is “left over” when an integer is divided by a non-zero integer. For example, the division of 11 by 7 results in 1 and leaves the remainder 4. In the terminology of number theory, this can be written as 11 ≡ 4 mod 7 (in words: 11 and 4 are congruent modulo 7 or, synonymously, 4 is a residue of 11 modulo 7) .
In general notation: a ≡ b mod m, expressing that the difference a-b is an integral multiple of m. The symbol b represents the remainder or residue.

Note: The German word for remainder or residue is the masculine noun Rest. Infrequently, the word rest can be found in English-language math texts, used as a synonym for remainder or residue.

Keywords: arithmetics, mathematics, number theory, division, English language, German language