2305199 is a prime number.
Use Fermat's little theorem,
2199 ≡ 2(mod 199)
Therefore,
21991 ≡ 210*2(mod 199) ≡ 58 (mod 199)
man111 singh Thanking you Shashwata Roy 
\hspace{-16}$Calculate The Remainder When $\bf{2^{2009}}$ is divided by $100$
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3 Answers
1357(1024)^201=(-1)^201 mod(25)
2^2010=-1 mod (25)
2^2010=24 mod (25)
2^2009=12 mod (25)
2^2009-12 is divisible by 25
it is also divisible by 4
So it is divisible by 100
So remainder is 12
- man111 singh Thanking You SirUpvote·0· Reply ·2013-02-22 01:30:04
23051708Sir I have another Question.
\hspace{-16}$Calculate the remainder when $\bf{2^{1991}}$ is divided by $\bf{199}$\\\\