Value of \(2^{48}\)(mod 15); is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
A small power of 2 leaves remainder 1 when divided by 15:
\(2^4 = 16 = 15 + 1\)
\(2^4 \equiv 1 \pmod{15}\)
Since \(48 = 4 \times 12\):
\(2^{48} = \left(2^4\right)^{12}\)
\(2^{48} \equiv 1^{12} = 1 \pmod{15}\)