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4 divides x_1x_2+x_3x_3+...+x_{n-1}x_n+x_nx_1 -n

Source: Netherlands - Dutch NMO 1974, year 1974-75 (also named as 1975 -1) p2

January 27, 2023
number theorydividesdivisible

Problem Statement

n>2n>2 numbers, x1,x2,...,xn x_1, x_2, ..., x_n are odd . Prove that 44 divides x1x2+x2x3+...+xn−1xn+xnx1−n. x_1x_2+x_2x_3+...+x_{n-1}x_n+x_nx_1 -n.
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