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NT III Problems not answered in class

 
 
JinTina的头像
NT III Problems not answered in class
JinTina - 2023年05月13日 Saturday 16:11
 

Hello!


I need some help on 5.30 5.32, and 5.33. For 5.32, I tried using mod 3, but I don't know what else to do. For 5.33, I figured out all (n-2)5+(n-1)5+5n+5(n+1)+5(n+2) works, but when not "consecutive" multiples of 5 are put in, I don't know if it works. At 5.30, I don't know what to do.


Thanks!


Tina Jin

 
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Re: NT III Problems not answered in class
JinTina - 2023年05月20日 Saturday 18:34
 

Hello,


Problems 5.32 and 5.33 were answered, but I still need some help on 5.30

 
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WangDr. Kevin的头像
Re: NT III Problems not answered in class
WangDr. Kevin - 2023年05月27日 Saturday 00:23
 

For 5.30, you can use the following fact (try to prove it): Assume a polynomial $P(x)$ has integer coefficients.  Let $m$ and $n$ be integers, then $P(m)-P(n)$ is divisible by $m-n$.

For the problem itself, find $P(62)-P(19)$, and see what the above fact gives you.

 
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