Square each integer \(n\) in the range \(1\le n\le 10\) 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?

1^2 /11 = R 1

2^2 /11 = R4

3^2 /11 = R9

4^2 /11 = R 5

5^2 /11 = R 3

6^2 /11 = R 3

7^2/11 = R 5

8^2 / 11 = R9

9^2 /11 = R 4

10^2 /11 = R1

m = [ 1 + 4 + 9 + 5 + 3 + 3 + 5 + 9 + 4 + 1 ] = 44 / 11 = 4

CPhill: When he/she says "add up all the distinct results", does that mean "no duplicates"?

Mmmmm...yes.... I missed that...

The distinct results are

1 + 4 + 5 + 9 + 3 =

22 = m

m / 11 = 2

Thanks, guest...for catching that....!!!