1. E

    Problem (Bezout's theorem/GCD)

    Hello, can you help me solve this problem? It's urgent please: Let 1 <= m <= n be two integers. Note by C (n; m) = (n!) / ((n-m)! m!) Show that (gcd (n, m) / n) (C (n, m)) is an integer. Tip: Bézout's theorem. Thank you.
  2. Z

    Bezout's Identity converse

    Bezout's Identity: If d = gcd(m,n), there exist integers A and B st d=Am+Bn. (proved by Euclid's algorithm} 1) Is there a converse? 2) How would you express it? 3) How would you prove it?
  3. E

    Bezout's identity and odd co primes

    Good evening, Let a and b two odd positive integers >1 and e = +1 or -1, is it true that... ...these propositions are equivalent : 1) a and b are co primes 2) there exist two odd positive integers, u<b, v<a such au-bv = 2e 3) there exist two odd positive integers, x<b, y<a such by-ax = 4e...