Modulus Problem

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
## Seems that R and Fermat disagree

## Also,
1000000000000000000 %% 11
[1] -32

This seems like a bug. Should I be avoiding integer math for large
numbers?

You can find out the largest representable integer from 
.Machine$integer.max, and it is probably 2^31-1.  Numbers larger than that 
are converted to double precision.  On the other hand, %% should probably 
return an error or NaN if .Machine$double.eps times the first operand is 
greater than 1.

 	-thomas

Hi

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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