- #1
whodsow
- 12
- 0
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.
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.
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.