Tudily7735 Tudily7735
  • 09-07-2018
  • Mathematics
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Question: determine all solutions to the diophantine equation 3x + 7y = 4

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sqdancefan
sqdancefan sqdancefan
  • 09-07-2018
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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