Mathematical and Physical Journal
for High Schools
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Problem A. 517. (October 2010)

A. 517. Let m\ge3 be a positive integer, and let \Phim(x) be the mth cyclotomic polynomial, and denote by \Psim(x) the polynomial with integer coefficients for which x^{\varphi(m)/2} \Psi_m\left(x+\frac1x\right) = \Phi_m(x). Prove that for every integer a, any prime divisor of the number \Psim(a) either divides m or is of the form mk\pm1.

(5 pont)

Deadline expired on November 10, 2010.


5 students sent a solution.
5 points:Backhausz Tibor.
4 points:Ágoston Tamás, Nagy 235 János, Nagy 648 Donát.
3 points:1 student.

Problems in Mathematics of KöMaL, October 2010