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222 ^ 222, divided by 7, what is the remainder ?

+1 vote

222 ^ 222, divided by 7, what is the remainder ?

asked Oct 11, 2014 in TCS by Hasan Mandal

1 Answer

+1 vote
 
Best answer
We can use fermat little theorem to solve this question.
$\displaystyle\frac{{{{222}^{222}}}}{7} = \frac{{{5^{222}}}}{7}$
Fermat's little theorem = $\displaystyle\frac{{{a^{p - 1}}}}{p} = 1$
Here P should be prime
So $\displaystyle\frac{{{5^{222}}}}{7} = \frac{{{{\left( {{5^6}} \right)}^{37}}}}{7} = \frac{{{1^{37}}}}{7} = 1$
So the remainder is 1.
answered Oct 15, 2014 by Campusgate
explain again plz
why it is written as 5^222
Divide 222 by 7. Remainder is 5.
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