Mathematical and Physical Journal
for High Schools
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Problem A. 513. (September 2010)

A. 513. For what primes p does there exist a cubic polynomial f with integer coefficients with the property that p does not divide the leading coefficient of f and f(1),f(2),...,f(p) give pairwise distinct remainders modulo p?

Proposed by Péter Maga

(5 pont)

Deadline expired on November 10, 2010.


11 students sent a solution.
5 points:Ágoston Tamás, Backhausz Tibor, Frankl Nóra, Kalina Kende, Mester Márton, Nagy 235 János, Nagy 648 Donát, Strenner Péter.
4 points:Lenger Dániel, Szabó 928 Attila.
1 point:1 student.

Problems in Mathematics of KöMaL, September 2010