Time to Compare

Number Theory Level 2

$A = 7^{10^{10^{10}}}$ $\pmod 6$

$B = 6^{10^{10^{10}}}$ $\pmod 7$

What can we say about $A$ and $B$ ?

Note: $0\leq A<6$ and $0\leq B<7$ .

None of the given choices A < B A = B A > B

1 solution

Hana Wehbi
May 13, 2016

7 to any power in mod 6 has a remainder of 1.

6 to an even power divided by 7 has a remainder of 1.

Another Solution:

$6^{2n} mod\ 7$ = $36^{n} mod\ 7$ = $1^{n} mod \ 7$ = 1 $mod\ 7$

and $7 ^{n} mod\ 6$ = $1^ {n} mod\ 6$ = 1 $mod\ 6$

Perfect solutionl

Ashish Menon - 5 years ago