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Find all integer solutions to each of the following Diophantine equations: 1. 15. X +9.Y = 162. 2. 21 X 9. Y = 18.

Find all integer solutions to each of the following Diophantine equations: 1. 15. X +9.Y = 162. 2. 21 X 9. Y = 18. 3. 21 X +9. Y = 23. 4. 4 X+ 6 Y + 10 - Z = 17. 5. 4. X+6. Y + 10 Z = 18. You should do this by hand, but you may check your work using sage.

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1 Number of solutions found 4 X 1 0 Y 1 18 X 2 3 Y 2 13 X 3 6 Y 3 8 X 4 9 Y 4 3 2 Number of solutions found 452 X 1 0 Y 1 2 X 2 3 Y 2 5 X 3 6 Y 3 12 X 4 9 Y 4 19 X 5 12 Y 5 26 X 6 15 Y 6 33 X 7 18 Y 7 ... blur-text-image

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