22 Jun
2005
22 Jun
'05
12:47 p.m.
"Chris" == Chris Landauer <cal@rushg.aero.org> writes:
Chris> the function is also not multiplicative, since mod 4 period 6 Chris> mod 7 period 16 mod 28 period 48 Correct. What IS true is that if n1, n2, ..., nk are relatively prime, then fp(n1*n2* ... * nk) = lcm(fp(n1),fp(n2), ..., fp(nk)). This is easily seen by noticing that fp(n) is the multiplicative order of (1+sqrt(5))/2 in (Z/n)[(1+sqrt(5))/2]*, which, by the Chinese Remainder Theorem (do we need the fact that Z[(1+sqrt(5))/2] has unique factorization?) breaks up into the product of (Z/ni)[(1+sqrt(5))/2]*. Victor