Question

What is the remainder when \(\large 4444^{4444}\) is divided by \(\large 9\)?

Answer 1

start taking digital remainders

Answer 2

in the exponents \(4+4+4+4=16\) and \(1+6=7\) so the remainder when you divide \(4444\) by \(9\) is \(7\)

Answer 3

therefore the remainder of \(4444^{4444}\) when divided by \(9\) is the same as the remainder of \(7^7\) when divided by \(9\)

Answer 4

you have some more work to do to finish, but i hope that part was clear enough

Answer 5

well not much actually
\[7^7=49^3\times 7\] should finish it up nicely

Answer 6

i see :)
Thank you

Answer 7

nice :)

\[\large 4444^{4444} \equiv (4\times 11\times 101)^{4444} \equiv 2^{4444} \mod 9\]