Haskell - Computations (2) P68540

These problems are inspired in some of the problems from Project Euler. You can find them at https://projecteuler.net.

1. The sum of the squares of the first 10 natural numbers is 1²+2²+…+10²=385. The square of the sum of the first 10 natural numbers is (1+2+…+10)²=55²=3025. Therefore, the difference between the sum of the squares of the first 10 natural numbers and the square of the sum of the first 10 natural numbers is 3025 − 385 = 2640.

   Write a function diffSqrs :: Integer -> Integer that, given a natural n, returns the difference between the sum of the squares of the first n natural numbers and the square of the sum of the first n natural numbers.

2. A Pythagorean triplet are three natural numbers (a,b,c) such that a²+b²=c². Write a function pythagoreanTriplets :: Int -> [(Int, Int, Int)] that, given a natural n≥1, returns the list of all Pythagorean tripletes that add up to n. Each triplet must be sorted in such a way that a≤ b≤ c and the list must be sorted according to a.
3. Write a function tartaglia :: [[Integer]] that returns an infinite list with the rowss of the Tartaglia’s triangle (also known as Pascal’s triangle).
4. Write a function sumDigits :: Integer -> Integer that returns the sum of all digits of a natural number. Use high order functions rather than recursion.
5. Write a function digitalRoot :: Integer -> Integer that returns the digital root of a natural number. Use high order functions rather than recursion.

Scoring

Each function scores 20 points.