Compute the least positive residue $x$ such that
$$ 3^{101} \equiv x \pmod {103} $$
Since 103 is prime, and does not divide 3, we can use the FlT,
$ 3^{102} \equiv 1 \pmod {103}$
This gives us
$ 3^{102} \equiv 3x \equiv 1 \pmod {103} $
The first positive number that is congruent to 1 mod 103 is 104, but this is not a multiple of 3.
The next one is 207, which is $3 \times 69$.
And so $x \equiv 69 \pmod {103}$.