Prove $n^7-n$ is divisible by 7.
it's actually true for some $n^p-n$ but not proven for all p=prime.
Hint: multiplication of 7consecutive numbers divisible by 7.
7 divide $n^7-n$
- Tahmid Hasan
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- Nadim Ul Abrar
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Re: 7 divide $n^7-n$
n^6=1 mod 7
=> n^7/n= 1 mod 7
=> n^7-n=0 mod 7
=> n^7/n= 1 mod 7
=> n^7-n=0 mod 7
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Re: 7 divide $n^7-n$
do u please can explain it ? which theorem u use?
do anyone can solve it without induction?
do anyone can solve it without induction?
Re: 7 divide $n^7-n$
nadim used fermat's little theorem
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Re: 7 divide $n^7-n$
Does he can prove it for all $n^p-n$ ?
Re: 7 divide $n^7-n$
The fact is whether we can use fermat's theorem or not.
One one thing is neutral in the universe, that is $0$.