Simple Concept Tough Problem – 5

Hello readers ! We are at the fifth problem in the SCTP series. This problem had appeared in the PRMO 2018 paper. Here is the problem :

Integers a,b,c satisfy a+b-c=1 and a^2+b^2-c^2=-1. Find the sum of all possible values of a^2+b^2+c^2.

We will see that this problem requires a basic property of divisibility of integers. If a and b are integers such that a divides b and b divides a, then a=b. Please see the following video for the detailed solution.