Number Theory

# Strategies for Number Theory Problems-1

Here is the first chapter of the series of articles I shall write about some strategies for olympiad-style problems. In this article I considered number theoretic problems only. The article is attached as a pdf below: Strategies-1-Number Theory-1

Correction : In exercise 1.1. it would be $n^2+19n+92$ in place of $n^2+19+92 .$

## 8 thoughts on “Strategies for Number Theory Problems-1”

1. Exercise 1.1. Find all integers n for which
n^2 + 19 + 92 is a square. I think it should be n^2+19n+92. Please confirm. I liked your article very much. It is really helpful for me!

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2. It would be good if you guys could provide solutions to some selected problems from the articles

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1. I shall add some solutions in the next chapter (number theory-2), specially those solutions which have some nice idea or insights.

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1. Thank you! Appreciate it!Btw ,this is Giffunk(AOPS)

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3. Vicky Ricky says:

Can u send me the solution to the problem 6.1 as i am not getting confirm whether my solution is correct or not.

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1. First note that y must be odd and x must be even say x=2z. Then 4(z^2+1)=(y-1)(y^2+y+1). Now 4 divides the RHS and y^2+y+1 is odd, so 4 divides y-1. Hence y^2+y+1=3(mod 4). This has a prime factorisation of the form 3(mod 4) which divides z^2+1, contradiction.

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1. Vicky Ricky says:

Thanks.

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