IMO LONGLISTED PROBLEM 1974

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MATHPRITOM
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IMO LONGLISTED PROBLEM 1974

Unread post by MATHPRITOM » Sat Nov 12, 2011 11:09 pm

Prove that,$2^{147}$-1 is divisible by 343.
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Ashfaq Uday
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Re: IMO LONGLISTED PROBLEM 1974

Unread post by Ashfaq Uday » Sun Nov 13, 2011 4:04 pm

we've to prove \[2^{147}=1(mod 343)\]
we know \[2^{9}=169(mod343)\Rightarrow 2^{144}=43(mod343)\]
and \[2^{3}=351(mod343)\]
multiplying both this we get the desired result.
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