[PDF] a^b mod n formula

For a positive integer n, two integers a and b are said to be congruent modulo n (or a is congruent to b modulo n), if a and b have the same remainder when divided by n (or equivalently if a ? b is divisible by n ). It can be expressed as a ? b mod n. n is called the modulus.
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  • What does a ? b mod m mean?

    BASIC PROPERTIES OF CONGRUENCES. The letters a, b, c, d, k represent integers. The letters m, n represent positive integers. The notation a ? b (mod m) means that m divides a ? b. We then say that a is congruent to b modulo m.

  • What is an example of a B mod N?

    For integers, "a?b (mod n)" means that a-b is a multiple of n. It is often written "a=b (mod n)". For example, 1, 8, 15, 22 are all equal mod 7. This is the basic idea in modular arithmetic, an extremely important idea in mathematics.

  • What does 1 mod n mean?

    In modular arithmetic, x ? 1 means that x and 1 belong to the same residue class. If you have a clock with N hour divisions, turning the hand 1 time or x times will bring the hand to the same end position. For your specific case, x ? 1 (mod N) can be represented as x % N === 1 in JavaScript if x is never negative.
  • a1 + a2 ? b1 + b2 (mod n) (compatibility with addition) a1 – a2 ? b1 – b2 (mod n) (compatibility with subtraction) a1 a2 ? b1 b2 (mod n) (compatibility with multiplication) ak ? bk (mod n) for any non-negative integer k (compatibility with exponentiation)
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