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(Solved): Let a,b,c,dinZ such that the matrix ([a,b],[c,d]) has an inverse whose entries are all integers. Le ...



Let

a,b,c,dinZ

such that the matrix

([a,b],[c,d])

has an inverse whose entries are all integers. Let

x,yinZ

such that at least one of them is not zero. Prove that

gcd(x,y)=gcd(ax+by,cx+dy).^(1)


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