Enough with the introductions! Let’s see some code!

```
-- Problem 31: Determine whether a given integer number is prime.
-- Armed with our experience from Project Euler, this is not very daunting.
-- We make sure n is not divided by any "candidates" up to sqrt(n). Which candidates?
-- Well, the prime numbers, of course! Well, we're not gonna spend time tracking out the
-- prime numbers in a primality test, though - we're going to use the P6 candidates;
-- numbers of the form 6*n±1 :
isprime :: (Integral a) => a -> Bool
isprime n | n < 4 = n > 1
isprime n = all ((/=0) . mod n) $ takeWhile (<=m) candidates
where candidates = (2:3:[x + i | x <- [6,12..], i <- [-1, 1]])
m = floor . sqrt $ fromIntegral n
-- Problem 32: Determine the greatest common divisor of two positive integers.
-- Enter Euclid:
mygcd a 0 = abs a
mygcd a b = mygcd b (a `mod` b)
-- Problem 33: Determine whether two positive integer numbers are coprime.
-- Straight from the definition of coprimality:
coprime a b = gcd a b == 1
-- Problem 34: Calculate Euler's totient function.
-- The definition makes it easy for us, again:
phi n = length [m | m <- [1..n-1], coprime m n]
```

The rest of the solutions have more actual commentary, plus they’re in progress, so we’ll leave them for later. Cheers!

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