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This is a Regional Mathematics Olympiad, RMO 2015 Problem 3 from West Bengal Region.

Actually, I had a typographical mistake in my last post i.e. question paper.

The 3rd post says to find integer solutions, not positive integer solutions.

I consider this problem as the easiest problem in RMO 2015. So let's discuss the solution...

**Problem**

**Source :- RMO 2015 West Bengal Problem 3**

Show that there are infinitely many triplets of integers such that

**Solution**

Let us put We get

Now, let be 2 integers, such that

If we put then we have

Which is true.

Hence, every triplet of the forms, where are integers, such that is a solution to the equation.

And, as takes infinitely many values, the equation has infinitely many solutions.

This completes the proof.

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Actually obviously it was asking for non zero triplets so its not that easy. You sould try for non zero integers, then it's a good question

Exactly.

But what to do... go through the other questions, you will understand.

I think, unexpected triviality might make it the deciding factor for cut-offs since many of the candidates could be trolled by this.