关于丢番图方程px4-(p-1)y2=z4

姜信君. 关于丢番图方程px4-(p-1)y2=z4[J]. 信阳师范学院学报(自然科学版), 2010, 23(1): 7-11.

引用本文:

姜信君. 关于丢番图方程px4-(p-1)y2=z4[J]. 信阳师范学院学报(自然科学版), 2010, 23(1): 7-11.

On the Diophantine Equation px4-(p-1)y2=z4[J]. Journal of Xinyang Normal University (Natural Science Edition), 2010, 23(1): 7-11.

Citation:

On the Diophantine Equation px4-(p-1)y2=z4[J]. Journal of Xinyang Normal University (Natural Science Edition), 2010, 23(1): 7-11.

On the Diophantine Equation px4-(p-1)y2=z4

摘要: 利用初等方法给出了丢番图方程px4-(p-1)y2=z4当p=qQ2+1,2|Q,q≡3(mod4),p、q为奇素数时的全部正整数解,从而拓展了王洪昌和王春光的px4-(p-1)y2=z4的结果.

Abstract: we give all positive integer solutions to the diophantine equation px4-(p-1)y2=z4 by the elementary methods on condition that p=qQ2+1,2|Q,q≡3(mod 4),p and q are odd prime number.Thereby we have extended the result of equation px4-(p-1)y2=z4 studied by Wang Hongchang and Wang Chunguang.

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