document: On the diophantine equation x/sup 2 / + q/sup 2k +1 / = y/sup n / In this paper it has been proved that if q is an odd prime , q not = 7 -LRB- mod 8 -RRB- , n is an odd integer > or = 5 , n is not a multiple of 3 and -LRB- h , n -RRB- = 1 , where h is the class number of the filed Q -LRB- square root -LRB- - q -RRB- -RRB- , then the diophantine equation x/sup 2 / + q/sup 2k +1 / = y/sup n / has exactly two families of solutions -LRB- q , n , k , x , y -RRB-
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