Show that if a,b,c are integers; c>0; and a [congruent] b(mod m), then gcd(a,c) = gcd(b,c)

Show that if a,b,c are integers; c>0; and a [congruent] b(mod m), then gcd(a,c) = gcd(b,c)

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Heres what I was thinking ...

and its a = b (mod c) .. typoed it

since a = b (c); then a = b + ck, for some integer k a - b = ck ax1 + bx2 = ck ax1 + bx2 = c(y1+y2) ax1 + bx2 = cy1 + cy2 ax1 + cy1 = bx2 + cy2 ax1 + cy1 = g1, for some integer g g1 = bx2 + cy2 gcd(a,c) = gcd(b,c)

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