We apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation x^2＋（3...We apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation x^2＋（3a^2-1）^m = （4a^2-1）^n when 3a^2-1 is a prime or a prime power.展开更多
Using the estimates of character sums over Galoi8 rings and the trace de-scription of primitive sequences over Z_(p^e), we obtain an estimate for the frequency of theoccurrences of any element in Z_(p^e) in one period...Using the estimates of character sums over Galoi8 rings and the trace de-scription of primitive sequences over Z_(p^e), we obtain an estimate for the frequency of theoccurrences of any element in Z_(p^e) in one period of a primitive sequence, which is betterthan Kuzmin's results if n >4e, where n is the degree of the generating polynomial ofthe primitive sequence.展开更多
基金the Natural Science Foundation of Guangdong Province (04009801)the Important Science Research Foundation of Foshan University.
文摘We apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation x^2＋（3a^2-1）^m = （4a^2-1）^n when 3a^2-1 is a prime or a prime power.
文摘Using the estimates of character sums over Galoi8 rings and the trace de-scription of primitive sequences over Z_(p^e), we obtain an estimate for the frequency of theoccurrences of any element in Z_(p^e) in one period of a primitive sequence, which is betterthan Kuzmin's results if n >4e, where n is the degree of the generating polynomial ofthe primitive sequence.
