Prove that $243^{2020} \equiv 1 \pmod 5$

Question

I was supposed to use that $a^4 \equiv 1 \pmod 5$, but that's not helping me, specifically, I don't know how to prove that $243^{505}$ is not as $5k, k \in \mathbb{Z}$.

Apply the first corollary in the linked dupe with $,e = 4.\ \ $ — Bill Dubuque, Nov 29 '20 at 00:32

score -1 · Answer 1 · answered Nov 29 '20 at 00:29

-1

$$243^{2020}=(243^4)^{505}\equiv (3^4)^{505}\equiv 1^{505}\equiv 1\pmod 5 $$

answered Nov 29 '20 at 00:29

Hagen von Eitzen

374,180

2

Please strive not to add yet more diupe answers to FAQs. – Bill Dubuque Nov 29 '20 at 00:33

Prove that $243^{2020} \equiv 1 \pmod 5$

1 Answers1