Question

I tried solving the following problem in haskell:

Find the smallest number b with (a^b
mod 100) = 1 for every a with
gcd(a,100)=1

I tried this:

head[ b | a <- [1..], b <- [1..], (a^b `mod` 100) == 1, gcd a 100 == 1]

but this yields 1^1 as the first solution, which is not correct, it should be for every ; 3^1 is not a solution for example.
I think the correct solution is b=20 but I want it in haskell.

Answer 1

Find the smallest number b

find f [1..]

with (a^b mod 100) = 1 for every a

f b = all (\a -> a^b `mod` 100 == 1) xs

[every a] with gcd(a,100)=1

    where xs = [a <- [1..100], gcd a 100 == 1]