Algebra - Remainder

1357

Manish Shankar ·2013-02-20 20:37:46

(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

2305

Shaswata Roy ·2013-02-22 02:02:31

199 is a prime number.

Use Fermat's little theorem,

2¹⁹⁹ â‰¡ 2(mod 199)

Therefore,

2¹⁹⁹¹ â‰¡ 2¹⁰*2(mod 199) â‰¡ 58 (mod 199)

1708

man111 singh ·2013-02-22 01:35:05

Sir I have another Question.

\hspace{-16}$Calculate the remainder when $\bf{2^{1991}}$ is divided by $\bf{199}$\\\\

Remainder