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Solve the diophantine equation: 7x+40y=1

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svjr | Student, Undergraduate | Honors

Posted November 8, 2011 at 2:55 AM via web

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Solve the diophantine equation: 7x+40y=1

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 8, 2011 at 4:23 AM (Answer #1)

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The Diophantine equation 7x + 40y = 1 only has integer solutions for x and y.

This can be solved using the following algorithm:

40 = 7*5 + 5......1 = 40*3 - 7*17

7 = 5*1 + 2........1 = -7*7 + 5*10

5 = 2*2 + 1 .......1 = 5*1 - 2*2

..........................1 = 0*2 + 1*1

This gives the solution of the equation as x = -17 and y = 3

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