\( 3^{16} \) (mod 4) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
Since 3 leaves remainder 3 on division by 4, and 3 − 4 = −1,
\( \displaystyle 3\equiv-1\pmod 4 \)
Raising both sides to the power 16:
\( \displaystyle 3^{16}\equiv(-1)^{16}\pmod 4 \)
\( \displaystyle \equiv1\pmod 4 \)
So \( 3^{16} \) (mod 4) = 1.