Math prep No 129 求助

littleblues

If t is a positive integer and r is the remainder when t² +5t+6 is divided by 7,what is the value of r?

1)when t is divided by 7,the remainder is 6

2) when t² is divided by 7,the remainder is 1

the key is A

为什么不是D 啊? 由二式中t² is divided by 7,the remainder is 1 可得t 是6 ，r的值是2

BruceNornia

t也可以是8阿....

BruceNornia

这个题目是这样的...

如果X除Y余数为Z 那么f(X)除Y的余数和f(Z)除Y的余数相同

所以这个题目里面f(t) = t² +5t+6 只要能知道t除7的余数一定能算出f(t)除7的余数 所以1）一定对

 

但是如果t²除7余1的话，t除7可以余1或者6

所以f(t)除7可以余5也可以余2

xiayizhang

t² is divided by 7,the remainder is 1---------t有很多可能 比方t=8