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Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands.
The fraction 13/5 = 2.6 and the floor function have that effect; the denominator of 5 sets a period of 5 months. The overall function, mod 7 {\displaystyle \operatorname {mod} \,7} , normalizes the result to reside in the range of 0 to 6, which yields the index of the correct day of the week for the date being analyzed.
The constants R mod N and R 3 mod N can be generated as REDC(R 2 mod N) and as REDC((R 2 mod N)(R 2 mod N)). The fundamental operation is to compute REDC of a product. When standalone REDC is needed, it can be computed as REDC of a product with 1 mod N. The only place where a direct reduction modulo N is necessary is in the precomputation of R ...
S&DJR 7F 2-8-0. Factor of adh. 53809, at Green Park Station (now a car park) in Bath, 6 March 2006. The Somerset and Dorset Joint Railway (S&DJR) 7F 2-8-0 is a class of steam locomotive designed for hauling heavy coal and goods trains. Eleven were built in two batches in 1914 and 1925, and were used until withdrawal between 1959 and 1964.
Additive inverse. In mathematics, the additive inverse of an element x, denoted -x[ 1], is the element that when added to x, yields the additive identity, 0 [ 2]. In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element . In elementary mathematics, the additive inverse is often referred to as ...
Zolotarev's lemma. In number theory, Zolotarev's lemma states that the Legendre symbol. for an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation: where ε denotes the signature of a permutation and π a is the permutation of the nonzero residue classes mod p induced by multiplication ...
The so-called totatives 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is {1, 5, 7, 11}. The cardinality of this set can be calculated with the totient function: φ(12) = 4. Some other reduced residue systems modulo 12 are: {13,17,19,23} {−11,−7 ...