Question: determine all solutions to the diophantine equation 3x + 7y = 4

1 answer:

3 0

The difference between the coefficients 7 and 3 is 4, so one solution is
y = 1, x = -1.
Then the remaining solutions will be of the form
x = -7n-1
y = 3n+1
for some integer n.

_____
Some of the solutions are (for n=0, -1, -2, 1, 2)
(x, y) = (-1, 1), (6, -2), (13, -5), (-8, 4), (-15, 7)

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