## Exercise 1.1
```python
def zorglub(n: int) -> int:
	j = 1
	k = 0
	i = 1
	while i <= n:
		j = i * j
		k = j + k
		i = i + 1
	return k
```

The function return the sum of the factorial of n

## Exercise 1.2
```python
def multiplication(x: int, y: int) -> int:
	result = 0
	while y > 0:
		m += x
		y -= 1
	return result


def multiplication2(x: int, y: int) -> int: # Thanks Hugo :p
	if y < 0:
		y = -y
		if x < 0:
			return multiplication(-x, y)
		return -multiplication(x, y)			
	else
		return multiplication(x, y)

def productZ(x, y):
	pos = True
	if x < 0:
		x = -x 
		pos = False
	if y < 0:
		y = -y
		pos = not pos
	m = multiplication(x, y)
	if not pos:
		m = -m
	return m
```

## Exercise 1.3
```python
def exponetial(x: int, n: int) -> int:
	result = 0
	while n > 0:
		m *= x
		n -= 1
	return result

def power(x, n):
	if x == 0;
		if n == 0:
			raise Exception("0 power 0 undefinded")
		else:
			return 0
	elif x == 1:
		return 1
	elif x == -1:
		return (n%2)*(-2) + 1
	else:
		res = 1
		while n > 0:
			res *= x
			n -= 1
		return res
```

## Exercise 1.4

```python
def fibo(n):
	prev = 1 #f0
	cur = 1 #f1
	while n> 1:
		(prev, cur) = (cur, prev+cur)
		n -= 1
	return cur
# OR
def fibo(n):
	prev = 1
	cur = 1
	i = 1
	while i < n:
		prev += cur
		cur += prev
		i += 2
	if i == n: # i % 2 == 1
		return cur
	else: 
		return prev
```

## Exercise 1.5
1) 
```python
def my_sum(n: int) -> int:
	s = 0
	i = 1
	while i <= n:
		s += u(i)
		i += 1
	return s
# OR

def my_sum(n: int) -> int:
	s = 0
	while n > 0:
		s += u(n)
		n -= 1
	return s
```
2) 
```python
def my_sum(n: int) -> int:
	ss = 0
	i = 1
	while i <= n:
		si = 0
		j = 1
		while j <= i:
			si += u(j)
			j += 1
		ss += si
		i += 1
	return ss

# OR
def my_sum(n: int) -> int:
	ss = 0
	i = 1
	while i <= n:
		j = 1
		while j <= o:
			ss += u(j)
			j += 1
		i += 1
	return ss

# OR
def mu_sum(n: int) -> int:
	ss = 0
	si = 0
	i = 1
	while i <= n:
		si += u(i)
		ss += si
		i += 1
	return ss
```

## Exercise 2.1
```python
def euclid(a, b):
	if (a <= b):
		raise Exception("a must be superior to b")
	r = 1
	while r != 0:
		oldr = r
		q = a//b
		r = a%b
		a = b
		b = r
	return oldr

# OR
def euclid(a, b):
	while b != 0:
		(a, b) = (b, a%b)
	return a
```

## Exercise 2.2
```python
def mirror(n: int) -> int;
	res = 0
	while n != 0:
		res = res * 10 + n % 10
		n //= 10
	return res
```

## Exercise 2.3
```python
def factorial(limit: n) -> int:
	n = 0
	if limit <= n:
		return n
	else:
		f = 1
		while f < limit:
			n += 1
			f *= n
		if n % 2 == 0:
			return (n-2)
		else:
			return (n-1)
```

## Exercise 2.4
```python
def prime(n: int) -> int:
	"""
	Check if n(int) is prime if n > 1, error otherwise
	"""
	if n <= 1:
		raise Exception("prime: n<= 1")
	elif n % 2 == 0:
		return n == 2
	else:
		d = 3
		while d*d <= n and n % d!= 0:
			d += 2
		return d*d > n
```
## Exercise 3.3
```python
def quotient(a: int, b: int) -> int:
	q = 0
	if (a < b):
		(a, b) = (b, a)
	while (a-b) >= 0:
		q += 1
		a -= b
	return q