Maths Olympiad Prep

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, 2021

Algebra Difficulty 5.0 AIME, harder Prove it United Kingdom

A sequence of integers a1,a2,a3,a_1, a_2, a_3, \ldots is defined by
a1=k,a_1 = k,
an+1=an+8n for all integers n1.a_{n+1} = a_n + 8n \text{ for all integers } n \ge 1.
Find all values of kk such that every term in the sequence is a square.

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