Solve the diophantine equation: 15x+64y=1

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justaguide eNotes educator| Certified Educator

The Diophantine equation: 15x+64y=1 can have only integer solutions for x and y.

For 15x+64y=1, apply the following algorithm

64 = 15*4 + 4.......1 = 64*4 - 15*17

15 = 4*3 + 3.........1 = -1*15 + 4*4

4 = 3*1 + 1...........1 = 1* 4 - 3*1

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

The solution of the equation is x = -17 and y = 4

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