1. The problem statement, all variables and given/known data For all integers n, it is impossible to have a solution to the equation 4^n = a^2 + b^2 + c^2 where a, b and c are all positive integers. (Hint: Notice that 4^n = 2^2n is a perfect square. Show (prove) that if m^2 = a^2 + b^2 + c^2, then we must have that a, b and c are all even. This can be done without induction; just think about what remainders a perfect square can leave when divided by four.) 2. Relevant equations None in accordance from the chapter. I'm in a discrete mathematics course and this problem's chapter is on Induction. With the previous chapter before it was dealing with standard logic proofs. 3. The attempt at a solution The only idea I could think of to attempt with is using the proof method of induction just like how I have used in the previous problems of my homework. By induction proof method, I mean the procedure of plugging in "n=1", to see if the proposition is true and continuing after by plugging in "n+1" etc. I'm just not sure how to adjust this problem to solve it by using induction.