[SOLVED] larsen problem 1. The problem statement, all variables and given/known data Determine all integral solutions of [itex]a^2+b^2+c^2=a^2 b^2[/tex]. (Hint: Analyze modulo 4.) 2. Relevant equations 3. The attempt at a solution a^2,b^2,c^2 are congruent to 0 or 1 mod 4 implies that a^2,b^2,c^2 are all congruent to 0 mod 4. This implies that a,b,c are even. [tex]a=2a_1, b=2b_1, c=2c_1[/tex] Then we have [itex]a_1^2+b_1^2+c_1^2 = 4a_1^2 b_1^2[/itex]. Now it is very clear that a_1^2,b_1^2,c_1^2 are all congruent to 0 mod 4. Let [itex]a_1=2a_2,b_1=2b_2,c_1=2c_2[/itex]. If we keep doing this, we get 3 decreasing sequences of positive integers that never reach zero, which is impossible. Therefore there are no solutions. Is that right?