Divisibility of a sequence by 10100

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Dipta Akash Roy
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Divisibility of a sequence by 10100

Unread post by Dipta Akash Roy » Wed Jan 11, 2012 2:16 pm

Show that $1^5+2^5+3^5+\cdots+100^5$ is divisible by $10100$ ;)
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Moon
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Re: Divisibility of a sequence by 10100

Unread post by Moon » Wed Jan 11, 2012 7:05 pm

Show that $S=1^5+2^5+3^5+\cdots+100^5$ is divisible by $100$ and $101$ separately. Also use $x^5 \equiv-(101-x)^5 \pmod{101}$ etc.
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Dipta Akash Roy
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Re: Divisibility of a sequence by 10100

Unread post by Dipta Akash Roy » Wed Jan 11, 2012 11:07 pm

Thanks. Now its very easy.
X=V-E+F
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