haskell列表理解（数论问题）

find f [1..]

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

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

import Data.Numbers.Primes

carmichael 1 = 1
carmichael 2 = 1
carmichael 4 = 2
carmichael n | isPowerOf 2 n    = n `div` 4
             | isPowerOf fac1 n = (n `div` fac1) * (fac1 - 1)
             | otherwise        = foldr1 lcm $ map (carmichael . product) grp
  where factors@(fac1:_) = primeFactors n
        grp              = group factors

isPowerOf n k | n == k         = True
              | k `mod` n == 0 = isPowerOf n (k `div` n)
              | otherwise      = False

bs = [b | b <- [1..],
         (and [(a `mod` b)==1 | a <- [1..])
     ]

a <- [1..]

and

False

[ (x,y) | x <- [0,1], y <- [0,1] ] == [(0,0),(0,1),(1,0),(1,1)]
[ (x,y) | x <- [0,1], y <- [0..] ] == [(0,0),(0,1),(0,2),(0,3),(0,4),(0,5),...]
[ (x,y) | x <- [0..], y <- [0,1] ] == [(0,0),(0,1),(1,0),(1,1),(2,0),(2,1),...]

a

b

[ (a,b) | a <- [1..], b <- [1..] ] == [(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),...]