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## #1 2017-10-10 00:21:31

Arman Ansary
Member
Registered: 2017-10-07
Posts: 4

### Check your knowledge: A really good problem

This question was given, when I was preparing, by my teacher.
He gave 15 minutes.

Let 'a' and 'b' be positive integers such that (ab + 1) divides (a^2 + b^2).
Then show that :
(a^2 + b^2) ÷ (ab + 1) is a square of an integer.

DON'T ATTEMPT IF YOU HAVE DONE BEFORE OR ELSE IT WOULD PROVE TOO EASY.

I could only figure the half way, my sir helped me out.

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## #2 2017-10-10 00:23:56

Arman Ansary
Member
Registered: 2017-10-07
Posts: 4

### Re: Check your knowledge: A really good problem

Can we post pictures or else its hard to give geometry problems?

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## #3 2017-10-10 00:25:25

Arman Ansary
Member
Registered: 2017-10-07
Posts: 4

### Re: Check your knowledge: A really good problem

Arman Ansary wrote:

Can we post pictures or else its hard to give geometry problems?

But this not of that category, so no difficulty.

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