Prove this equation has no integer solutions: $x^p_{1}+x^p_{2}+\cdots+x^p_{n}+1=(x_{1}+x_{2}+\cdots+x_{n})^2$

Modulo $2$, the LHS is congruent to $x_1 + \cdots + x_n + 1$ while the RHS is congruent to $x_1 + \cdots + x_n$.

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Number Theory

Quadratic Residues

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