Find The Remainder
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
What will be the remainder if you divide $72^{1001}$ by $31$ ?
Last edited by *Mahi* on Mon Apr 16, 2012 12:09 am, edited 1 time in total.
Reason: LaTeXed
Reason: LaTeXed
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
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- Posts:190
- Joined:Sat Apr 23, 2011 8:55 am
- Location:Khulna
Re: Find The Remainder
Use fi function .
- Phlembac Adib Hasan
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Re: Find The Remainder
\[72^{1001}\equiv 72^{11}\equiv 10^{11}\equiv 10.(10^2)^5\equiv 10.7^5\equiv 168070\equiv 19(mod\; 31)\]
Where the first congruence follows from Fermat's little theorem.
Where the first congruence follows from Fermat's little theorem.
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