Question

if "u" is the remainder of 13 ^ 2 ^ 2011 is divided by 16, then the value of 2u-5 is?

plissss plissss :(

Answer 1

the remainder will either be 1 or 9. you can check that the remainder when you divide 13^2 by 16 is 9, and when you divide 13^4 by 9 the remainder will be 1. the pattern continues.

Answer 2

because 2011 is odd, the remainder will be 9, and so know u = 9, and therefore you can easily find 2u - 5

Answer 3

how to get 9??
plisss

Answer 4

how to get 9??

Answer 5

i simply checked. i checked that if you divide 13^2 by 16 i got a remainder of 9

Answer 6

then i checked that if you divide 13^4 by 16 i get a remainder of 1

Answer 7

there may be a snappier way to do it, but i did it the donkey way. once i have the 1, i am done because the pattern has to continue

Answer 8

(13^2)^2011 mod 16
=169^2011 mod 16
euler 16=8
=169^(8k+3)mod16
=1.(169^3)mod16
=9 mod 16, u=9

how???

Answer 9

i did it the bonehead way. you can maybe try
\[13^(4022)==x (mod 16)

Answer 10

confused :D i will try again :D

Answer 11

13^{4022} equivalent with 13^{2} so its remainder is 9 :D

Answer 12

owh i know now ^_^