Modular equation
in [Math]
|
Prev: On Coast to Coast AM this morning, the topic was the Shroud of Turin. ... bend, fold, staple, and mutilate.
Next: Impersonators Flatter Me, Thank YOu
From: bert on 6 Apr 2010 05:10 On 6 Apr, 00:14, "joe.doubtful" <joe.doubt...(a)yahoo.it> wrote: > On 5 Apr, 23:00, bert <bert.hutchi...(a)btinternet.com> wrote: > > > > > > > On 5 Apr, 21:38, "joe.doubtful" <joe.doubt...(a)yahoo.it> wrote: > > > > On 5 Apr, 22:12, "joe.doubtful" <joe.doubt...(a)yahoo.it> wrote: > > > > > Hi, consider the modular equation s^4 = -4 mod q, where q=3 mod 4. > > > > Does anyone knows how to prove that it has no solutions? > > > > Thanks in advance > > > > I forgot: q is an odd prime. > > > Let t = s^2 / 2, then t^2 = -1 mod q, > > so what you want is the existing and > > well-known proof that -1 is a quadratic > > residue of only those primes of the form > > 4n+1, not of primes of the form 4n+3. > > -- > > Interesting, I didn't know that result. A last question: how do you > know that s is even? See Rob Johnson's reply. Or, to put it less theoretically, if s and s^2 are odd, then (s^2 + q) is even, so t will come out as a whole number; all the arithmetic is mod q. -- |