We prove that if d is a triangular number congruent to 3 mod.4, then the equation x-y=d has a finite number of solutions with x, y both perfect numbers. We outline a general approach to determine the exact number of solutions and show that there is none for d=3,15
Ramanujan-Nagell type equations and perfect numbers
ELLIA, Filippo Alfredo;
2015
Abstract
We prove that if d is a triangular number congruent to 3 mod.4, then the equation x-y=d has a finite number of solutions with x, y both perfect numbers. We outline a general approach to determine the exact number of solutions and show that there is none for d=3,15File in questo prodotto:
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