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On the diophantine equation x2 + p2k = yn
被引：0
作者：
Attila Bérczes
István Pink
机构：
[1] University of Debrecen,Institute of Mathematics
[2] Number Theory Research Group,undefined
[3] Hungarian Academy of Sciences and University of Debrecen,undefined
来源：
Archiv der Mathematik
|
2008年
/
91卷
关键词：
Exponential diophantine equations;
primitive divisors;
11D41;
11D61;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let 2 ≤ p < 100 be a rational prime and consider equation (3) in the title in integer unknowns x, y, n, k with x > 0, y > 1, n ≥ 3 prime, k ≥ 0 and gcd(x, y) = 1. Under the above conditions we give all solutions of the title equation (see the Theorem). We note that if in (3) gcd(x, y) = 1, our Theorem is an extension of several earlier results [15], [27], [2], [3], [5], [23].
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页码：505 / 517
页数：12
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