Proof 5∣n<=>5∣n^2

Leia Hood

Leia Hood

Answered question

2022-08-09

Proof
5 n 5 n 2

Answer & Explanation

beentjie8e

beentjie8e

Beginner2022-08-10Added 20 answers

Hints:
( ) If a b then a b c.
( ) 5 is a prime number; use Euclid's lemma.
sunnypeach12

sunnypeach12

Beginner2022-08-11Added 5 answers

Assume 5 n then n = 5 k for some k Z which means n 2 = 25 k 2 = 5 5 k 2 therefore 5 n 2 . For the other direction assume that 5 n 2 . A square modulo 5 is congruent to either 0 or 1 or 4 which can be used to show the other direction.

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