AoPS - Problem

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Problem

Source: HK TST1 2009, Problem 6

Tags: modular arithmetic, number theory unsolved, number theory

lchserious

20.08.2008 10:13

Show that the equation $y^{37}\equiv x^3+11 \pmod p$ is solvable for every prime $p$ , where $p\leq100$ .

ZetaX

20.08.2008 15:38

It is at least (but not at most) solvable for all primes $p \not\equiv 1 \mod 37$ and $p \not\equiv 1 \mod 3$ , thus by all primes not $\equiv 1 \mod 111$ . By the way, it is solvable for all but finitely many primes.