Thread: Possible remainders

What are possible remainders when dividing with 9 squares of natural numbers?

Originally Posted by OReilly

What are possible remainders when dividing with 9 squares of natural numbers?

You can attack the problem with Division Algorithm.

Meaning any number must be exactly in one of these forms,



.........................


When you square then, you get, the only possibilities,




Thus, remainders are 0,1,4,7

I must say I didn't think of that!
This problem has destroyed me! Whole day I couldn't solve it. Problems with divisibility are giving me most hard times and usually I can't solve them!