**Question:** Use the fact that $10^2 = 100$ and $11^2 = 121$ to show that the number 101 is a prime number. 

Could someone please given me a hint on how to solve this problem. I can't seem to relate $11^2=121$ to the fact that 101 is a prime number. I thought of using theorem of gcd or modular arithmetic, but I don't know where to start.