matt ran 8 laps in 1,256 seconds if he ran each lap in the same amount of time how many seconds did it take him to run 1 lap
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Note that 1111 is not divisible by 3, so it follows that 
(they are coprime). Given that 
, where 
is the Euler totient/phi function, and that
we can then write
By Euler's theorem, we have
and so
Note that
which means
so
.
we can then write
By Euler's theorem, we have
and so
Note that
which means
so