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The least non-negative remainder when $2^{75}$ is divided by 5 will be:- |
1 2 3 4 |
3 |
The correct answer is Option (3) → 3 To find $2^{75} \bmod 5$: By Fermat’s theorem: $2^{4} \equiv 1 \pmod{5}$ Now, $75 = 4 \cdot 18 + 3$ $\Rightarrow 2^{75} \equiv (2^4)^{18} \cdot 2^3 \equiv 1^{18} \cdot 8 \equiv 8 \pmod{5}$ $8 \bmod 5 = 3$ Answer: 3 |
