#### Exercise 1 || Solution

Write an algorithm in python which exchanges two integers m and n entered on the keyboard and which displays the values of the numbers before and after the exchange operation.

#### Exercise 2 || Solution

Write a program in Python that asks the user to enter two numbers a and b and display their sum: a + b.

#### Exercise 3 || Solution

Write a program in Python that asks the user to enter two numbers a and b and to display their maximum.

#### Exercise 4 || Solution

Write a program in Python language that displays the first 100 integers

#### Exercise 5 || Solution

Write a program in Python language that asks the user to enter their

integer number and to display it if this number is even or odd.

#### Exercise 6 || Solution

Write a program in Python language that asks the user to enter their age

and display the message "You're Major!" If the age typed is greater

than or equal to 18 and the message "you are under age!" If the typed

age is less than 18

#### Exercise 7 || Solution

Write a program in Python that asks the user to enter 3 numbers x, y, and z and display their maximum

#### Exercise 8 || Solution

Write a program in Python that asks the user to enter an integer n and display the value of the sum 1 + 2 + ... + n =

#### Exercise 9 || Solution

Write a program in Python that asks the user to enter an integer n and display it n!

#### Exercise 10 || Solution

Write a program in Python that asks the user to enter the radius of a circle and return the area and perimeter.

#### Exercise 11 || Solution

Write a program in Python that asks the user to enter an integer n and display all the divisors of that number.

#### Exercise 12 || Solution

**1) -** Write a program in Python that asks the user to enter an integer n and display the multiplication table of that number.

**2) -** Improve the program so that it displays multiplication tables of all numbers between 1 and 9

#### Exercise 13 || Solution

Write a program in Python language that asks the user to enter two

integers a and b and to display the quotient and the remainder of the

Euclidean division of a by b.

#### Exercise 14 || Solution

Write a program in Python language that asks the user to enter an

integer n and display it if this number is perfect square or not.

#### Exercise 59 || Solution

Write an algorithm in python which finds the list of all even integers

from a given integer m to another given integer n.

Example for m = 10 and n 15, the searched list is L = [10, 12, 14]

#### Exercise 60 || Solution

Write an algorithm in python which determines the list of all relative integers n <= 1000 such that n + 7 divides 3n^{5} + 19.

#### Exercise 62 || Solution

Create a program in Python that tests whether a given integer is sum of two perfect squares. Example the **integer n = 13** is sum of two perfect squares** 13 = 2 ^ 2 + 3 ^ 2.**

#### Exercise 63 || Solution

Write a program in Python language that asks the user to enter an integer n and display it if this number is prime or not.

#### 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.**

#### Exercise 82 || Solution

write a python program which calculates the number of pairs of integers (i, j) verifying:

** **

**50 <= i + j <= 50 ^ 2**

#### Exercise 83 || Solution

Write an algorithm in python that computes a factorial of an integer recursively without using the for loop.

#### Exercise 84 || Solution

write a python algorithm as a function which takes as argument an integer n and which returns the number of tuples (u, v, w) of integers such that u, v and w are all divisors of n and n = u + v + w. Example for n = 18 the list of sought tuples is:

L = [(3, 6, 9), (3, 9, 6), (6, 3, 9), (6, 6, 6), (6, 9, 3), (9, 3, 6), ( 9, 6, 3)]

#### Exercise 85 || Solution

Write an algorithm in Python which determines the list of all pairs of relative integers (x, y) verifying the equation :

xy - x - y = n

for a given integer n. give the result for n = 19.

#### Exercise 86 || Solution

Write a Python algorithm that determines the list of all

common divisors of two given integers m and n.

**Younes Derfoufi
my-courses.net
**