[R] Modulus Problem

[Robin Hankin]

Hi
On Dec 8, 2004, at 04:59 pm, McGehee, Robert wrote:

> R users, I am having a problem with the modulus operator for large
> numbers as follows,
>
> a <- 2
> n <- 561
> ## n is the first Carmichael number, so by Fermat's Little Theorem the
> below should equal zero.
>
> (a^(n-1) - 1) %% n
> [1] 2.193172e+152
>

I don't think Fermat's Little Theorem is relevant here.  Euler's 
theorem would be though:
a^phi(561)=1 (mod 561) where phi is the totient function.

For your problem, try this:

f <- function(a,p){
   a <- as.integer(a)
   p <- as.integer(p)
   out <- as.integer(1)
   for(i in 1:p){
     out <- (out*a)%%p
   }
   return(out)
}


Then



 > f(2,561)
[1] 1
 > f(3,561)
[1] 375        (sic)
 > f(5,561)
[1] 1
 >


best

rksh

> ## Seems that R and Fermat disagree
>
> ## Also,
> 1000000000000000000 %% 11
> [1] -32
>
> Thi______________________________________________
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--
Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743