I found a rule that the equation ax + by = (a-1)(b-1), for gcd(a, b)=1, has a solution in integers x and y with x ≥ 0 and y≥0, but the equation ax + by = (a-1)(b-1) - 1 don't.(adsbygoogle = window.adsbygoogle || []).push({});

For example, the equation 3x + 7y = 12 has such soluntion (x, y) = (4, 0), but 3x + 7y = 11 has no such solutions that x and y are integers with x ≥ 0 and y≥0.

I have verified more a and b, which show my conjecture is correct, but I cann't prove that.

please help me, thanks.

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# A question about the solution of linear equation

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