Find The Remainder

Fahim Shahriar · Unread post by **Fahim Shahriar** » Sun Apr 15, 2012 11:10 pm

What will be the remainder if you divide $72^{1001}$ by $31$ ?

MATHPRITOM · Unread post by **MATHPRITOM** » Mon Apr 16, 2012 7:42 am

Use fi function .

Unread post by **Phlembac Adib Hasan** » Mon Apr 16, 2012 9:06 am

\[72^{1001}\equiv 72^{11}\equiv 10^{11}\equiv 10.(10^2)^5\equiv 10.7^5\equiv 168070\equiv 19(mod\; 31)\]
Where the first congruence follows from Fermat's little theorem.

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