1. The problem statement, all variables and given/known data This question was asked in the Indian National Maths Olympiad. The question is: Find all the possible real ordered pairs of (x,y) for equation 16^[(x^2) + y] + 16^[x + (y^2)]=1 2. Relevant equations That was the only equation. 3. The attempt at a solution Using 0.5 + 0.5 =1, (x^2) + y = -0.25 and (y^2) + x= -0.25 (Because [16^(-0.25)]=0.5 , I'm using decimals here instead of fractions) Solving them gives one real ordered pair of (-0.5,-0.5). But how do I know if that's the only answer?