MathDB

P6

Part of 2016 India National Olympiad

Problems(1)

A non-constant AP with square of terms also as terms of AP

Source: INMO 2016 Problem 6

1/17/2016
Consider a nonconstant arithmetic progression a1,a2,⋯ ,an,⋯a_1, a_2,\cdots, a_n,\cdots. Suppose there exist relatively prime positive integers p>1p>1 and q>1q>1 such that a12,ap+12a_1^2, a_{p+1}^2 and aq+12a_{q+1}^2 are also the terms of the same arithmetic progression. Prove that the terms of the arithmetic progression are all integers.
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