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Abstract

Let h denote the class number of the quadratic field for a square free odd integer A &gt; 1, and suppose that n &gt; 2 is an odd integer with ( n , h ) = 1 and m &gt; 1. In this paper, it is proved that the equation of the title has no solution in positive integers x and y if n has any prime 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) .

Locations

• International Journal of Mathematics and Mathematical Sciences - View - PDF
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