Discuz Math Forum»Forum › Mathematics › High School › 求最大公因数

Return to list New

View 1774|Reply 2

[数论] 求最大公因数

[Copy link]

770 Threads	4692 Posts	310K Credits

Credits: 35048

Send PM

isee Posted 2014-9-4 08:15 |Read mode

集合$\{16^n+10n-1|n\in Z^*\}$的最大公因数是什么？

Reply Edit

413 Threads	1431 Posts	110K Credits

Credits: 11099

Send PM

realnumber Posted 2014-9-4 08:57

n=1,是25
$(15+1)^n+10n-1=25k+15n+1+10n-1=25k+25n$,k是某整数，二项展开。
所以答案是25.

Reply Edit

770 Threads	4692 Posts	310K Credits

Credits: 35048

Send PM

Author| isee Posted 2014-9-4 08:59

回复 2# realnumber

被秒了。。。

Reply Edit

Return to list New

Mobile version|Discuz Math Forum

2025-5-31 10:52 GMT+8

Powered by Discuz!

× Quick Reply To Top Edit