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| Paper IPM / M / 8009 |
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| Abstract: | |||||
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Let p be an odd prime such that p−3 is not a perfect square.
In this paper we prove that the equation x2+3=pyp−1 has no
solutions in rational numbers x,y. The proof depends on the
unique factorization in the ring of algebraic integers of
\mathbbQ(√−3) and on certain congruence arguments.
Furthermore, the equations x2+3=py[(p−1)/2] and
x2+3=py6 in rationals x,y are also considered.
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