4

Part of 2015 EGMO

Problems(1)

EGMO P4 infinite sequence

Source: EGMO 2015, Problem 4

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

number theorySequenceEGMOInteger sequenceHi