| Erd■s一个猜想的注记 |
| |
| 引用本文： | 吴昌玖,王鹏飞. Erd■s一个猜想的注记[J]. 成都大学学报(自然科学版), 1994, 0(2) |
| |
| 作者姓名： | 吴昌玖 王鹏飞 |
| |
| 作者单位： | 万县师专，成都大学 |
| |
| 摘 要： | 当ｋ≥２，２ｋｎ＋１＝ｑｈ，ｑ≡－１（ｍｏｄ２ｋ），丢番图方程４／ｎ＝ｘ－１十ｙ－１＋ｚ－１有正整数解；当方程中ｎ换以素数Ｐ，则Ｐ存疑的条件是Ｌｅｇｅｎｄｒｅ符号有（Ｐ／３）＝（Ｐ／５）＝（Ｐ／７）＝（Ｐ／１１）＝（Ｐ／１３）＝（Ｐ／１７）＝１．
|
| 关 键 词： | Erd s猜想，同余，Legengre符号，平方剩余 |
Remarks on a Conjecture of Erd■s |
| |
| Abstract: | In this note,we hsve proved the following Theorem 1 Let k≥s,and 2kn+1=qh, q=-1, (mod2k ). Then Diophantine equation 4/n =1/x+1 /y +1/z is soluable in positive integers x, y, z.Theorem 2 The condition that Diophantine equation 4/p=1/x+1/y+1/z (p is a primenumber) has indeterminable soluable is (p/3)= (P/5) =(P/7 )= (P/9)= (P/13 )= (P/17 )= 1. |
| |
| Keywords: | |
| 本文献已被 CNKI 等数据库收录！ |
|
