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a_{n+4} is the units digit of a_n+a_{n+3}

Source: VIII - Mathematics Regional Olympiad of Mexico Northeast 2008 P3

September 17, 2022
number theoryDigits

Problem Statement

Consider the sequence 1,9,8,3,4,3,…1,9,8,3,4,3,… in which an+4a_{n+4} is the units digit of an+an+3a_n+a_{n+3}, for nn positive integer. Prove that a19852+a19862+…+a20002a^2_{1985}+a^2_{1986}+…+a^2_{2000} is a multiple of 22.
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