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s_{i+1} = |s_i - s_{i-1}|

Source: CJMO 2023 p1, Canadian Junior Mathematical Olympiad 2023 /1

March 24, 2024
algebra

Problem Statement

Let aa and bb be non-negative integers. Consider a sequence s1s_1, s2s_2, s3s_3, .... . . such that s1=as_1 = a, s2=bs_2 = b, and si+1=∣si−si−1∣s_{i+1} = |s_i - s_{i-1}| for i≥2i \ge 2. Prove that there is some ii for which si=0s_i = 0.
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