## Tuesday, June 30, 2020

Python Mathematics: Arithmetic Exercises

#### Exercise 64 ||  Solution

Write two Python functions  quotient() and remainder() which takes two numbers a and b as parameters such that :
1. The function quotient() return the quotient q of the Euclidean division of a by b (without using the operator '//' )
2. 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

Write a Python function that takes as argument an integer n and that return the list of all divisors of n.

#### 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.

Younes Derfoufi
my-courses.net 