Open AccessOn the Diophantine equation Ax2 + 22m = yn
Author(s) -
Fadwa S. Abu Muriefah
Publication year - 2001
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/s0161171201004835
Subject(s) - diophantine equation , mathematics , integer (computer science) , prime (order theory) , prime factor , combinatorics , modulo , class number , field (mathematics) , quadratic equation , discrete mathematics , geometry , pure mathematics , computer science , programming language
Let h denote the class number of the quadratic field ℚ(−A) for a square free odd integer A>1,and suppose that n>2 is an odd integer with (n,h)=1 and m>1. In this paper, it is proved that the equation of the titlehas no solution in positive integers x and y if n has anyprime factor congruent to 1 modulo 4. If n has no such factor it is proved that there exists at most one solution with x and y odd. The case n=3 is solved completely. A result of E.Brown for A=3 is improved and generalized to the case where A is a prime ≢7(mod8)
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