| 阶为平方数的单群个数 |
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| 引用本文： | 邓辉文. 阶为平方数的单群个数[J]. 西南师范大学学报(自然科学版), 1997, 22(6): 735-737 |
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| 作者姓名： | 邓辉文 |
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| 作者单位： | 西南师范大学计算机科学系 |
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| 摘 要： | 阶为平方数的有限单群在最大素因子小于１０４００时仅有１２个，由此推出Ｄｉｏｐｈａｎｔｉｎｅ方程ｐ２－２ｑ２＝－１在ｐ，ｑ均为素数且小于１０４００时，仅有下列四个解：（ｐ，ｑ）＝（７，５），（４１，２９），（６３０１８０３８２０１，４４５６０４８２１４９），（１９１７５００２９４２６８８０３２９２８５９９，１３５５８７７４６１００４６７１１７８０７０１）．
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| 关 键 词： | 有限群；单群阶；Diophantine方程；方程的解 |
The number of finite simple groups whose orders are squares |
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| Deng Huiwen. The number of finite simple groups whose orders are squares[J]. Journal of southwest china normal university(natural science edition), 1997, 22(6): 735-737 |
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| Authors: | Deng Huiwen |
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| Abstract: | There are only 12 finite simple groups whose orders are squares when the largest prime of the group order is less than 10 400 . From it, it is known that if p and q are primes and less than 10 400 , then the Diophantine equation p 2-2q 2 =-1 has only four solutions: (p, q) =(7, 5), (41, 29), (63018038201, 44560482149), (19175002942688032928599, 13558774610046711780701). |
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| Keywords: | finite groups orders of simple groups Diophantine equations solutions of equations |
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