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Miklós Schweitzer 1955- Problem 7

Source:

October 8, 2015
number theorycollege contests

Problem Statement

7. Prove that for any odd prime number pp, the polynomial
2(1+xp+12+(1−x)p+12)2(1+x^{ \frac{p+1}{2} }+(1-x)^{\frac {p+1}{2}})
is congruent mod pp to the square of a polynomial with integer coefficients. (N. 21)
*This problem was proposed by P. Erdõs in the American Mathematical Monthly 53 (1946), p. 594
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