IMO LONGLISTED PROBLEM 1974
Posted: Sat Nov 12, 2011 11:09 pm
Prove that,$2^{147}$-1 is divisible by 343.
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.