Let x be an integer and let d be a

bacasauvfl

bacasauvfl

Answered question

2022-04-28

Let x be an integer and let d be a factor of 2x21. Prove that d21mod16

Answer & Explanation

hoppledhsy

hoppledhsy

Beginner2022-04-29Added 13 answers

If d is a factor of 2x21, then any ' factor p of d is a factor of 2x21.
Prime p>2 is a factor of 2x212 is a quadratic residue modulo p.
p±1mod8. Obviously 2 is not a factor of 2x21.
So d is a factor of 2x2-1d±1mod8d21mod16
The last equivalence follows because if 8d±1 then 16(d+1)(d1)=d21.

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