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EGMO P4 infinite sequence

Source: EGMO 2015, Problem 4

April 17, 2015

number theorySequenceEGMOInteger sequenceHi

Problem Statement

Determine whether there exists an infinite sequence

a_1, a_2, a_3, \dots

of positive integers which satisfies the equality

a_{n+2}=a_{n+1}+\sqrt{a_{n+1}+a_{n}}

for every positive integer

n