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greatest common divisor

Source: Bulgarian Math Olympiad MO 2004, problem 5

May 17, 2004
geometryrhombusnumber theory unsolvednumber theory

Problem Statement

Let a,b,c,da,b,c,d be positive integers such that the number of pairs (x,y)∈(0,1)2(x,y) \in (0,1)^2 such that both ax+byax+by and cx+dycx+dy are integers is equal with 2004. If gcd⁡(a,c)=6\gcd (a,c)=6 find gcd⁡(b,d)\gcd (b,d).
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