1. The problem statement, all variables and given/known data prove that 11^2 does not devide n^2+3n+5; for any n. In order for this to make sense n must be an integer. 2. Relevant equations 3. The attempt at a solution want to show that n^2+3n+5 is not congruent to 0(mod 121) Assume towards a contradiction that 11^2 divides n^2+3n+5 we can rewrite n^2+3n+5=(n+7)(n-4)+33. since i assumed that 11^2|n^2+3n+5 then 11^2|(n+7)(n-4)+33 (now is the part that i am not sure about) but 11^2 does not divide 33. Therefore 11^2 does not divide n^2+3n+5. I am not sure about this last step in the argument. thanks for any help.