المحاضرة الثامنة التطابقات congruences

#number_theory #congruences #modulo #mod #congruent #a=b(modm) Another approach to divisibility questions is through the arithmetic of remainders, or the theory of congruences as it is now commonly known. The concept, and the notation that makes it such a powerful tool Definition :. Let n be a fixed positive integer. Two integers a and b are said to be congruent modulo n, symbolized by a ≡ b (mod n) if n divides the difference a − b; that is, provided that a − b = kn for some integer k To fix the idea, consider n = 7. It is routine to check that 3 ≡ 24 (mod 7) − 31 ≡ 11 (mod 7) − 15 ≡ −64 (mod 7) because 3 − 24 = (−3)7, −31 − 11 = (−6)7, and −15 − (−64) = 7 · 7. When n | (a − b), we say that a is incongruent to b modulo n, and in this case we write #التطابقات #باقي_القسمة #aum