MathDB

7

Part of 1974 IMO Shortlist

Problems(1)

Prove that the greatest common divisors are equal

Source:

9/22/2010
Let ai,bia_i, b_i be coprime positive integers for i=1,2,…,ki = 1, 2, \ldots , k, and mm the least common multiple of b1,…,bkb_1, \ldots , b_k. Prove that the greatest common divisor of a1mb1,…,akmbka_1 \frac{m}{b_1} , \ldots, a_k \frac{m}{b_k} equals the greatest common divisor of a1,…,ak.a_1, \ldots , a_k.
least common multiplegreatest common divisornumber theory