Re: [PrimeNumbers] Help needed
- On Monday 31 January 2005 08:56, you wrote:
> Decio,Mike: you're giving me too much credit here, I was just throwing stuff in the
> Yes, you're right: that formula for B3 with gamma in it is just the key to
> David's stupendous calculation - see his pages (communicated off-list):-
air to see whether anyone brighter than me could figure it out. Truth be
told, I'm still working out the Postscript file written by David -- as the
joke goes, don't drink and derive...
[Non-text portions of this message have been removed]
- Let q a positive integer and 1<=r<=q. Is there a theorem that tells
us how many integers a, 1<=a<=q, verify a^r=1 mod(q)?
I have found that:
(1) if q is prime or a power of a prime p, i.e. q=p^x, then there
are GCD(r,EulerPhi(q)) integers a that satisfy a^r=1 mod(q).
(2) if q is a product of two powers of primes p' and p'', i.e.
q=p'^x p''^y, then there are GCD(r,Carmichael(q))*GCD(r,Phi
(q)/Carmichael(q)) integers a that satisfy a^r=1 mod(q).
Are these results correct and can we generalize to any integer q?
Thanks for your help