Remainder of Power Division

CAT 2002 Slot 1 · QA · Easy · Number System

When $2^{256}$ is divided by $17$ , the remainder would be:

Answer

$2^{256} = (2^4)^{64} = 16^{64}$ . $16 \equiv -1 \pmod{17}$ . So, $16^{64} \equiv (-1)^{64} \equiv 1 \pmod{17}$ . The remainder is 1.

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