Math Help - finding the remainder

1. finding the remainder

how do we do such problems?

like...

find the remainder when $3^{37}$ is divided by 79...

or when $4^{101}$ is divided by 101...

whats the method?

2. Originally Posted by adhyeta
how do we do such problems?

like...

find the remainder when $3^{37}$ is divided by 79...

or when $4^{101}$ is divided by 101...

whats the method?

Easy way to solve such problem is like

since 3^4=81 we have to take value greater than 79 hence (3^4)^9*3 = 3^37

3^4/79 = 81/79 leaves remainder 2 hence 2^9 *3 / 79 = 512*3 = 1536/79 will leaves a reminder 35

I hope it is Easy solution (think of binomial expansion)

3. Originally Posted by ADARSH
hence (3^4)^9*3 = 3^37
dint get this

4. Originally Posted by adhyeta
dint get this
${(3^4)^9}*3 = 3^{37}$