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a^2_1+a^2_2+ ...+a^2_N is a perfect square, find recurrence formula

Source: Austrian Federal Competition For Advanced Students 2004, Part 2, p4

August 30, 2019
Perfect SquareSequencerecurrence relationnumber theory

Problem Statement

Show that there is an infinite sequence a1,a2,...a_1,a_2,... of natural numbers such that a12+a22+...+aN2a^2_1+a^2_2+ ...+a^2_N is a perfect square for all NN. Give a recurrent formula for one such sequence.
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