Question

calculate

Answer 1

\[3^{64}\mod 67\]

Answer 2

by repeated squaring or fermat theorem or otherwise

Answer 3

3^4 = 81 = 14 mod 67

Answer 4

http://www.woodmann.com/forum/archive/index.php/t-6124.html

Answer 5

(14*14) = 62 mod 67

Answer 6

or -5 mod 67 might be simpler to work with

Answer 7

can this simplify to a number

Answer 8

it eventually goes to 15 i believe

Answer 9

from
3^64 mod 67
3433683820292512484657849089281 mod 67

I got 15? Check with everyone else...

Answer 10

ye,15 is correct

Answer 11

Great! You got it then

Answer 12

3^(64) mod 67

(3^4)^16 mod 67

(14)^16 mod 67

(14^2)^8 mod 67

(-5)^8 mod 67

(25)^4 mod 67

(22)^2 mod 67

15 mod 67

Answer 13

15 mod 67 = 15

Answer 14

can we use fermat little theorem

\[a^{p-1}\equiv 1\mod p\]

Answer 15

64 = 66-2 so maybe

Answer 16

\[3^{66}\equiv 1\mod 67\]
\[3^23^{64}\equiv 1\mod 67\]

Answer 17

so we just need to invert 9 mod 67. You can either do this by the Euclidean algorithm, or
by inspection. For example, 67 · 2 + 1 = 135 = 15*9

Answer 18

wat is the \[9^{-1}\equiv 15\mod 67\]