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Junior Regional Olympiad - FBH 2015 Grade 8 Problem 4

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October 1, 2018
number theoryIrreducible

Problem Statement

Let nn be a positive integer and a=2n⋅7n+1+11a=2^n\cdot 7^{n+1}+11 and b=2n+1⋅7n+3b=2^{n+1}\cdot 7^n+3. a)a) Prove that fraction ab\frac{a}{b} is irreducible b)b) Prove that number a+b−7a+b-7 is not a perfect square for any positive integer nn
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