## 17 May 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.

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