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f_n=[2^n\sqrt{69}]+[2^n\sqrt{96}]

Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p2 sl-2 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 14, 2022
number theory

Problem Statement

For natural nn, define fn=[2n69]+[2n96]f_n=[2^n\sqrt{69}]+[2^n\sqrt{96}] Prove that there are infinite even integers and infinite odd integers that appear in number f1,f2,…f_1,f_2,\dots.
(tatari/nightmare)
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