2-2024-x-mod-10-

Question Number 206025 by cortano12 last updated on 05/Apr/24

2^{2024} = x (m o d 10)

Answered by BaliramKumar last updated on 05/Apr/24

Find unit digit

2^{2024} = 2^{4 k + 4} = 2^{4} = 16 \Rightarrow 6

Answered by Rasheed.Sindhi last updated on 05/Apr/24

2^{2024} = x (m o d 10)

2^{4} \equiv 6 (m o d 10)

2^{2024} \equiv x (m o d 10)

\Rightarrow 2^{4 \times 506} \equiv x (m o d 10)

\Rightarrow {(2^{4})}^{506} \equiv x (m o d 10)

\Rightarrow {(6)}^{506} \equiv x (m o d 10)

O b s e r v e t h a t 6^{k} \equiv 6 (m o d 10) \forall k \in N

∴ 6^{506} \equiv 6 (m o d 10)

∴ {(2^{4})}^{506} \equiv 6 (m o d 10)

∴ 2^{2024} \equiv 6 (m o d 10)