1. The problem statement, all variables and given/known data Does there exist an integer n, such that 1+2+3+...+n, ends with the last two digits 13? 2. Relevant equations 1+2+3+...+n = n(n+1)/2 3. The attempt at a solution I reached a conclusion that 1+2+3+...+n [itex]\equiv 13 (mod 100)[/itex]. Also the sum has to be greater than 100, but from here I am stuck. What do I do?