Question

Find the remainder when 2^1990 is divided by 1990.

Answer 1

@mayankdevnani

Answer 2

Mod arithmetic :')
@terenzreignz

Answer 3

Why me? :/

Answer 4

Because you.

Answer 5

In this question How to square to so much power ?

Answer 6

Might have to resort to totients..... @ParthKohli ?

Answer 7

Sir if i use the exponent rule will it work here ?

Answer 8

Ah! Euler's Theorem!

Answer 9

factor 1990 first

Answer 10

Time to doodle...
\[\large 2^{1990}=4^{995}\]

Answer 11

How to factor it ?

Answer 12

how to factor 1990?

Answer 13

What is 4^5?
\[\Large = 1024^{199}\]

Answer 14

Yes @satellite73

Answer 15

try \(2\times 5\times 199\)

Answer 16

1990 = 10*199 = 2* 5* 199

Answer 17

\[\large 1024^{199}=1024\cdot 1024^{198}=1024\cdot 2048^{99}\]

Answer 18

try \(2\times 5\times 199\) means ?

Answer 19

Now let's start working some "mod magic" and reduce the bases at mod 1990
\[\Large =_{(mod \ 1990)} \ \ 1024\cdot 58^{99}\]