Simple Concept Tough Problem - 5

Debashish Sharma

May 18, 2020 • 2 min read

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.

Sign up for more like this.