## Re: Cyclotomic polynomial puzzles

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• ... Perhaps because the mods have set that as the on-line default? I tried to reply, but maybe I forgot that trap. There is no way of telling, since the
Message 1 of 43 , May 10, 2009
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> Why's everyone only replying off-list?

Perhaps because the mods have set that as the on-line default?
I tried to reply, but maybe I forgot that trap.
There is no way of telling, since the default
reply is not even copied to oneself.

Here goes again (sorry if it eventually appears twice):

> 3a) Can you categorise p,q,r such that Phi(pqr) only has
> coefficients in {-1,0,1}?
>  b) Can you find a bigger pqr with that property than
> anyone else?

pqr=
103534127524074104115541098969958708089926902711923091490097\
001545810093892338679248846099390229911806167096020172161339\
248099921117956336949559455817976090558652472327237037907245\
079673380295270552412505821551314360478060083799787164050405\
497609391864910896620579324752947949306589953853514558460087\
480667962113549945569489945478510973601172041512307421653813\
8676796204064794079723241321918976844647423

has a cyclotomic polynomial that is easily proven to be flat,
once you have factorized pqr into its 3 constituent primes.
Yet I believe that I am the only person in the world
who can actually prove that Phi(pqr) is indeed flat,
if the CIA has not yet spooked my hard drive.

Proof:

print(concat(isprime([p,q,r]),[pqr==p*q*r,r>q,q>p,Mod(r,q*p)^2==1]))
[1, 1, 1, 1, 1, 1, 1]

David (with thanks to Nathan)
• ... On who regularly publishes, in mathematical journals, articles that do not derive principally from other subjects, such as physics. David (pleading not
Message 43 of 43 , May 23, 2013
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