Question

Some body check my work please

find the remainder using fermat little theorm

\(\large\tt \color{black}{\dfrac{8^{122}}{19}}\)

Answer 1

\(\large\tt \color{black}{8^{122}mod19}\)

\(\large\tt \color{black}{8^{19\times 6+8}mod19}\)

\(\large\tt \color{black}{8^{8}mod19}\)

\(\large\tt \color{black}{64^{4}mod19}\)

\(\large\tt \color{black}{7^{4}mod19}\)

\(\large\tt \color{black}{(49\times49)mod19}\)


\(\large\tt \color{black}{\large\tt \color{black}{(11\times11=121)}mod19}\)

\(\large\tt \color{black}{=7}\)

Answer 2

i want to know if this is correct way of applying fermat

Answer 3

@zepdrix

Answer 4

@cj49

Answer 5

yeah, a^k mod k = 1

Answer 6

a>1

Answer 7

a is an integer

Answer 8

do i have to find the multiple of 19 in the index of 8 ?

Answer 9

ok thanks

Answer 10

you did fine

Answer 11

oops sry lol

Answer 12

i think its
\(\large\tt \color{black}{a^{p-1}\bmod{p}\equiv 1\bmod{p}}\)