- 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):-

>

> http://physics.open.ac.uk/~dbroadhu/cert/cohenb3.txt

> http://physics.open.ac.uk/~dbroadhu/cert/cohenb3.ps

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...

Décio

[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

Hervé