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## #1 Re: Maths Is Fun - Suggestions and Comments » Check your knowledge: A really good problem » 2017-10-10 00:25:25

Arman Ansary wrote:

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

But this not of that category, so no difficulty.

## #2 Re: Maths Is Fun - Suggestions and Comments » Check your knowledge: A really good problem » 2017-10-10 00:23:56

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

## #3 Maths Is Fun - Suggestions and Comments » Check your knowledge: A really good problem » 2017-10-10 00:21:31

Arman Ansary
Replies: 2

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.

## #4 Maths Is Fun - Suggestions and Comments » Remainder Theorem » 2017-10-07 18:17:40

Arman Ansary
Replies: 3

This was in my book:
The remainder when x^45 is divided by x^2 - 1 is :-
a)2x
b)-x
c)0
d)x
e)None of these

THIS WAS UNDER THE LEVEL 1 QUESTION SECTION.
Try to answer and it would be good if you show the method.