While iterations X38759

You have to program several functions. Do not use the math module.

1. Write an integer function int_root(n) that given a natural number n returns ⌊√n⌋.
2. Write a function int_log(a, b) that given natural numbers a greater than one and b greater than zero returns natural k such that a^k ≤ b < a^{k + 1}.
3. Write a function gcd_lcm(a, b) that given natural numbers a and b such that a≠ 0 or b≠0 returns the greatest common divisor and the least common multiple. Your code has to implement the Euclid’s algorithm.
4. Write a boolean function is_prime(n) that given a natural number n returns True if and only if n is prime.
5. In order to play table games at the casino you need some tokens. Red tokens cost 7 euros and yellow tokens cost 4. Write a function buy_tokens(n) that given a number n of euros such that n ≥ 20, it returns the equivalence in tokens. When several equivalences are possible the function returns the one minimizing the total number of tokens.
6. Write a function inv_factorial(n) that given an integer n > 1 it returns the number m such that (m − 1)! < n ≤ m!.

Scoring

The first function counts 15 points. Other ones count 17 point each one.