Solution
= Solution
Write $a=6r+1$ and $b=6s+1$. Then $ab=6(6rs+r+s)+1$, so $\boxed{ab\equiv1\pmod6}$. Repetition gives the same result for any finite product of numbers congruent to one.
= Solution
Write $a=6r+1$ and $b=6s+1$. Then $ab=6(6rs+r+s)+1$, so $\boxed{ab\equiv1\pmod6}$. Repetition gives the same result for any finite product of numbers congruent to one.