Q4 DEFINITION

Each of the numbers x1, x2, ...... xn , n ≥ 4, is equal to 1 or —1. Suppose, 
x1 X2 X3 X4 + X2 X3 X4 X5 + X3 X4 X5 X6 ......  Xn-3 Xn-2 Xn-1 Xn + Xn-2 Xn-1 Xn X1+ Xn-1Xn X1X2 + Xn X1 X2 X3 =0, then

a) n is even

b) n is odd

c) n is an odd multiple of 3

d) n is prime

Each term has to be either 1 or –1.

Hence, if the sum of n such terms is 0, then n is even

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