On the Diophantine equation $$\varvec{x^2+b^m=c^n}$$ x 2 + b m = c n with $$\varvec{a^2+b^4=c^2}$$ a 2 + b 4 = c 2

Nobuhiro Terai ()
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Nobuhiro Terai: Oita University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 1, 162-169

Abstract: Abstract Let a, b, c be pairwise relatively prime positive integers such that $$a^2 + b^4=c^2$$ a 2 + b 4 = c 2 and b is odd. Then we show that the equation of the title has only one positive integer solution $$(x, m, n)=(a, 4, 2)$$ ( x , m , n ) = ( a , 4 , 2 ) under some conditions.

Keywords: Diophantine equation; Integer solution; Pythagorean numbers; 11D61 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00162-0

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