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N =a_1a_2...a_n= 0 mod 3 if a_1-a_2 + a_3 -... + (-1)^{n-1}a_n = 0 mod 3

Source: 1969 Swedish Mathematical Competition p5

March 21, 2021
number theorydividesdivisible

Problem Statement

Let N=a1a2...anN = a_1a_2...a_n in binary. Show that if a1−a2+a3−...+(−1)n−1an=0a_1-a_2 + a_3 -... + (-1)^{n-1}a_n = 0 mod 33, then N=0N = 0 mod 33.
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