Discuz Math Forum»Forum › Mathematics › High School › 如何判断二次多项式是否存在平方数

Return to list New

View 1868|Reply 2

[数论] 如何判断二次多项式是否存在平方数

[Copy link]

81 Threads	434 Posts	12 Reputation

Send PM

tommywong posted 2014-7-12 11:17 |Read mode

$y=x^2+1=2,5,10,17,...$
$y=x^2+3=4,7,12,19,...$

现充已死，エロ当立。
维基用户页：https://zh.wikipedia.org/wiki/User:Tttfffkkk
Notable algebra methods：https://artofproblemsolving.com/community/c728438
《方幂和及其推广和式》数学学习与研究2016.

Reply Edit 0

2 Threads	57 Posts	0 Reputation

Send PM

caijinzhi posted 2014-7-12 14:35

二次剩余！？

Reply Edit

412 Threads	1432 Posts	3 Reputation

Send PM

realnumber posted 2014-7-12 21:24

回复 2# caijinzhi

1楼举的例子，如果$a>b>1,a,b\in N$,那么$a^2-b^2=(a-b)(a+b)\ge3$,
所以4是唯一一个了．

Reply Edit

Return to list New

Quick Reply

× Quick Reply To Top Edit

2025-7-23 01:43 GMT+8

Powered by Discuz!

Processed in 0.012825 seconds, 22 queries