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. 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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