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We show that if c is a positive integer satisfying $$2c-1=3p^l\ \hbox{or}\ 2c-1=5p^l$$ with p prime and l positive integer, then the equation $${x^2 + (2c-1)^m}=c^n$$ has only the positive… Click to show full abstract
We show that if c is a positive integer satisfying $$2c-1=3p^l\ \hbox{or}\ 2c-1=5p^l$$ with p prime and l positive integer, then the equation $${x^2 + (2c-1)^m}=c^n$$ has only the positive integer solution $$(x,m,n)=(c-1,1,2)$$ without any congruence condition on a prime p.
Keywords:
nagell equation;
generalized ramanujan;
ramanujan nagell;
positive integer;
equation
Journal Title: Acta Mathematica Hungarica
Year Published: 2020
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Journal Title: Acta Mathematica Hungarica
Year Published: 2020
Link to full text (if available)
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recommendations!