x, y are integers, and 17 divides both the expressions x²-2xy+y²-5x+7y and x²-3xy+2y²+x-y.

Does 17 always divide xy-12x+15y, for every choice of x and y?

If not, give an example.
If so, prove it.

Answer: Yes, xy-12x+15y is always divisible by 17 under the given conditions; for example, x=3080, y=1719 is just one possible solution.

The proof is straightforward and is left to the reader.

Posted by broll on 2015-04-26 12:39:00