Math, asked by SherlockHolmes11, 1 year ago

what is the remainder when 2^311 is divided by 19. Show full detailed answer.

Answers

Answered by manitkapoor2
2
Cool Question buddy
So we are going to use this trick formula
(a * b) %m = ((a%m)*(b%m))%m

so first base 2^10 mod 19 = 1024 mod 19 = 17
then 2^20 mod 19 = 17^2 mod 19  = 4
now 2^310 mod 19 = (17^31) mod 19 = (17^2)^15 * 17 mod 19
= 4^15 * 17 mod 9 
now 4^5 mod 19 = 17
so 4^15 * 17 mod 9 = (4^5)^3 17 mod 19 = 17^4 mod 19
= 16
so 2^310 mod 19 = 16
2^311 mod 19 = 16 * 2 mod 19 = 13

Anonymous286: congruence modulo method
Answered by brainlyvirat187006
2

Answer:

Cool Question buddy

So we are going to use this trick formula

(a * b) %m = ((a%m)*(b%m))%m

so first base 2^10 mod 19 = 1024 mod 19 = 17

then 2^20 mod 19 = 17^2 mod 19  = 4

now 2^310 mod 19 = (17^31) mod 19 = (17^2)^15 * 17 mod 19

= 4^15 * 17 mod 9 

now 4^5 mod 19 = 17

so 4^15 * 17 mod 9 = (4^5)^3 17 mod 19 = 17^4 mod 19

= 16

so 2^310 mod 19 = 16

2^311 mod 19 = 16 * 2 mod 19 = 13

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