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Prove that x_i is either 0 or 1

Source:

October 12, 2010

algebrapolynomialnumber theory unsolvednumber theory

Problem Statement

Let

n > 1

and

x_i \in \mathbb{R}

for

i = 1,\cdots, n

. Set

S_k = x_1^k+ x^k_2+\cdots+ x^k_n

for

k \ge 1

. If

S_1 = S_2 =\cdots= S_{n+1}

, show that

x_i \in \{0, 1\}

for every

i = 1, 2,\cdots, n.