10831 - Gerg's Cake
Given and , can a square cake be divided into equal sized pieces?
You have to test whether there is a solution to , where is an integer. Taking everything modulo , we get . Now we use a trick to get to Fermat's Little Theorem: we take everything to the power , so we get . So we only have to check whether . If it is, there is a solution and otherwise there isn't. This can easily be calculated in .
There are a few special cases, for example , and .
1 3 1024 17 2 101 0 1 -1 -1
Yes Yes No Yes