...arithmetic carried out modulo p. But first we review modular arithmetic in general. Definition Let АИ be a fixed positive integer. Two integers a and b are said to be congruent {modulo m), symbolized by a = b (modm), if a — b is divisible by m, ie if a = km + b for some integer k. We write...

...of integers. In so doing he created a new branch of number theory called the theory of congruences. Let m be a fixed positive integer. Two integers a and b whose difference a - b is divisible by m are said to be congruent with respect to the modulus m, or...

...2. Congruences. In this section we deal only with rational integers. Let m be an integer not zero. Two integers a and b are said to be congruent modulo m, written asb (mod m) or a = b (т) , if m ] (a — b) . If a and b are not congruent mod m we write a ^ b (m)...

...some definitions and basic properties from [3]. Let Z be the set of integers and -ft' be a strictly positive integer. Two integers a and b are said to be congruent modulo K, denoted by a = b[K] if and only if 3A e Z, b = a + \K. Denote a the unique element in [0, K —...