prove-that-if-an-integer-n-is-not-divisible-by-2-or-3-then-n-2-1-mod-24-

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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