jmc

Question

Square each integer n in the range 1 n 10 and find the remainders when the squares are divided by 11. Add up all the distinct results and call it m. What is the quotient when m is divided by 11?

Accepted Answer

First notice that (11-n)^2=11^2-2 11+n^2 n^211, and since we're asked to find distinct results, we only need to compute the squares of n=1,2,3,4,5. Respectively, n^2 1,4,9,5,311. Thus, 1+4+9+5+3=22=112.