modulo, prep. Math.
(ˈmɒdjʊləʊ)
[abl. of L. modulus.]
With respect to a modulus of. Also attrib., = modular.
| 1897 Bull. Amer. Math. Soc. III. 381 Congruences irreducible modulo p (p = prime). 1903 J. Bowden Elem. Theory Integers x. 242 The statement of congruence is written α ≡ β (mod. µ), which is read ‘α is congruent with β, modulo µ’ 1939 L. E. Dickson Mod. Elem. Theory Numbers i. 8 Any positive integer n is congruent modulo 9 to the sum s of its digits. 1966 Ogilvy & Anderson Excursions in Number Theory iv. 43 Since 8, 15, 22, 29, etc., and also —6, —13, etc. are all congruent to 1 (mod 7), they are members of the same residue class modulo 7... In arithmetic modulo 7, 8 is equivalent to 1 in many senses. Ibid. 44 In number theory one must often work with very large numbers. If these can be reduced to equivalent smaller numbers, much time-consuming labor can be avoided. Herein lies one of the great contributions of modulo arithmetic. 1971 J. H. Smith Digital Logic vi. 115 Modulo-7 counters count normally up to six (110). The next count must reset the counter to zero. 1973 Nature 20 Apr. 541/3 A sufficiently dense integer sequence is well distributed in most arithmetic progressions modulo most (small enough) primes. |