**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 \(n\).

# Welcome to EGMO 2018

The European Girls' Mathematical Olympiad is an international mathematical competition.

It addresses talented high school female students.