#### Exercise 64 || Solution

Write two Python functions **quotient()** and **remainder()** which takes two numbers a and b as parameters such that :

- The function
**quotient()**return the quotient q of the Euclidean division of a by b (without using the operator ‘//’ ) - The function
**remainder()**return the Euclidean division of a by b (without using the operator ‘%’

#### Exercise 65 || Solution

Write a function in Python which takes as argument a **tuple (a, b)** composed of two integers and returns it the **greatest common divisor GCD** of a and b without using any predefined function in python.

#### Exercise 66 || Solution

Write a function in Python which takes as argument a **tuple (a, b)** composed of two integers and returns it the **least common multiple LCM** of a and b without using any predefined function in python.

#### Exercise 67 || Solution

Write a function in Python which takes as argument an** integer n** and which returns **True** if the number **n is prim** and **False** if **n is not prim without using any predefined function.**

**Exercise 68 || Solution**

#### Exercise 69 || Solution

Write an algorithm as a function in Python which takes two integers a and b as arguments and returns True if the numbers a and b are coprime and False if not.

#### Exercise 70 || Solution

Write an Python algorithm which asks the user to type a **coprime intgeger n and m** and returns a **tuple (u, v)** verifying:** um + vn = 1** (**Bezout identity**)

#### Exercise 71 || Solution

Determine the list of odd divisors of the number 3570 which are multiples of 3 and contained in the interval [500, 2500]

#### Exercise 72 || Solution

Write an algorithm as python function which takes as parameters an integer n and which returns the last digit of n.

#### Exercise 73 || Solution

Write an algorithm as a python function that takes as parameters an integer n and which returns the list of divisors d whose last digit is equal to 1. Test your algorithm for n = 727821.

#### Exercise 80 || Solution

Write an algorithm in Python as a function which takes two numbers m and n as parameters (m < n) and which returns a list formed of all the prime numbers between m and n. Example for m = 10 and n = 20 the function must return

`[11, 13, 17, 19]`

#### Exercise 81 || Solution

Create a Python algorithm that calculates the** number of ways** to** pay 10 Euros**, using the **1 Euro, 2 Euro **and** 5 Euro coins.**

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