Expand Messages
• ... Mike: you re giving me too much credit here, I was just throwing stuff in the air to see whether anyone brighter than me could figure it out. Truth be
Message 1 of 8 , Jan 31, 2005
On Monday 31 January 2005 08:56, you wrote:
> Decio,
> 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):-
>

Mike: you're giving me too much credit here, I was just throwing stuff in the
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
Message 2 of 8 , Feb 4, 2005
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?