prove that if an integer n is not divisible by 2 or 3 then n^2 ≡1(mod 24)


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Question Number 217129 by ArshadS last updated on 02/Mar/25

$p r o v e t h a t i f a n i n t e g e r n i s n o t d i v i s i b l e b y 2 o r 3$ $t h e n n^{2} \equiv 1 (m o d 24)$
Commented by A5T last updated on 02/Mar/25

$This is not necessarily true .$ $n could also be \equiv 5, 7, 11, 13, 17, 19, 23 (\mod 24)$
Commented by ArshadS last updated on 02/Mar/25

$s i r q u e s t i o n h a s b e e n c o r r e c t e d .$
	Answered by A5T last updated on 02/Mar/25

	$2 ∤ n and 3 ∤ n \Rightarrow n \equiv 1, 5, 7, 11, 13, 17, 19 or 23 (\mod 24)$ $\Rightarrow n^{2} \equiv 1, 25, 49, 121, 169, 289, 361 or 529 (\mod 24)$ $which are all equivalent to 1 (\mod 24)$
	Commented by ArshadS last updated on 03/Mar/25

	$N i c e a p p r o a c h!$
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