1. The problem statement, all variables and given/known data Show that any power of two can be represented as 2^n=7*x^2+y^2 for some x,y odd. This problem was given to us in preparation for the final for an undergraduate number theory class. 2. Relevant equations 3. The attempt at a solution I tried numerical example to convince myself that it was true and to see if in the process i would get any ideas of how to approach this problem. But after many computations, i convince myself that it was true. but i could not come up with anything productive towards a proof. Thanks for your help.