The linear congruence ax = b (mod m)
has a solution if and only if (a,m) |b.
Prove it.
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hmm quite confusing wait a minutes let me solve
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If (a, m)=1, then the congruence ax ≡ b mod m phas exactly one solution modulo m. ... Note that ax ≡ b (mod m) implies ax = b + qm for some integer q. So a common divisor of a, m also divides b.
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