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What are all the solutions to the diophantine equation: 6x-6y-xy=0.

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    @Mily Why don't next time when you want to test something, instead of creating a new account and asking several similar questions in a row, you just tell people what your real problem is, and what you really want. This way, I believe, you will get more appropriate answers (I can't imagine how the two answers given here and for the other question might help to write the whole program solving Diophantine equations?!), and will also save some time for the moderators and others.2012-04-24

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Hint $\ $ Rewrite it as $\rm\: (6+x)(6-y) = 36.$

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The 18 integer solutions are :

x = -42, y = 7

x = -24, y = 8

x = -18, y = 9

x = -15, y = 10

x = -12, y = 12

x = -10, y = 15

x = -9, y = 18

x = -8, y = 24

x = -7, y = 42

x = -5, y = -30

x = -4, y = -12

x = -3, y = -6

x = -2, y = -3

x = 0, y = 0

x = 3, y = 2

x = 6, y = 3

x = 12, y = 4

x = 30, y = 5