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 $1^2+2^2+\dots+10^2=385$. The square of the sum of the first 10 natural numbers is $(1+2+\dots+10)^2=55^2=3025$. 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 $a^2+b^2=c^2$. Write a function pythagoreanTriplets :: Int -> [(Int, Int, Int)] that, given a natural $n\ge1$, returns the list of all Pythagorean tripletes that add up to $n$. Each triplet must be sorted in such a way that $a\le b\le c$ 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.