Project Euler Solutions in TheAlgorithms/Python

def solution(n: int = 4000000) -> int:
    """
    Returns the sum of all even fibonacci sequence elements that are lower
    or equal to n.

    >>> solution(10)
    10
    >>> solution(15)
    10
    >>> solution(2)
    2
    >>> solution(1)
    0
    >>> solution(34)
    44
    """

    i = 1
    j = 2
    total = 0
    while j <= n:
        if j % 2 == 0:
            total += j
        i, j = j, i + j

    return total

def is_prime(number: int) -> bool:
    """Checks to see if a number is a prime in O(sqrt(n)).
    A number is prime if it has exactly two factors: 1 and itself.
    Returns boolean representing primality of given number (i.e., if the
    result is true, then the number is indeed prime else it is not).

    >>> is_prime(2)
    True
    >>> is_prime(3)
    True
    >>> is_prime(27)
    False
    >>> is_prime(2999)
    True
    >>> is_prime(0)
    False
    >>> is_prime(1)
    False
    """

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5, int(math.sqrt(number) + 1), 6):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True

def solution(n: int = 998001) -> int:
    """
    Returns the largest palindrome made from the product of two 3-digit
    numbers which is less than n.

    >>> solution(20000)
    19591
    >>> solution(30000)
    29992
    >>> solution(40000)
    39893
    >>> solution(10000)
    Traceback (most recent call last):
        ...
    ValueError: That number is larger than our acceptable range.
    """

    # fetches the next number
    for number in range(n - 1, 9999, -1):
        str_number = str(number)

        # checks whether 'str_number' is a palindrome.
        if str_number == str_number[::-1]:
            divisor = 999

            # if 'number' is a product of two 3-digit numbers
            # then number is the answer otherwise fetch next number.
            while divisor != 99:
                if (number % divisor == 0) and (len(str(number // divisor)) == 3.0):
                    return number
                divisor -= 1
    raise ValueError("That number is larger than our acceptable range.")

def solution(n: int = 20) -> int:
    """
    Returns the smallest positive number that is evenly divisible (divisible
    with no remainder) by all of the numbers from 1 to n.

    >>> solution(10)
    2520
    >>> solution(15)
    360360
    >>> solution(22)
    232792560
    >>> solution(3.4)
    6
    >>> solution(0)
    Traceback (most recent call last):
        ...
    ValueError: Parameter n must be greater than or equal to one.
    >>> solution(-17)
    Traceback (most recent call last):
        ...
    ValueError: Parameter n must be greater than or equal to one.
    >>> solution([])
    Traceback (most recent call last):
        ...
    TypeError: Parameter n must be int or castable to int.
    >>> solution("asd")
    Traceback (most recent call last):
        ...
    TypeError: Parameter n must be int or castable to int.
    """

    try:
        n = int(n)
    except TypeError, ValueError:
        raise TypeError("Parameter n must be int or castable to int.")
    if n <= 0:
        raise ValueError("Parameter n must be greater than or equal to one.")
    i = 0
    while 1:
        i += n * (n - 1)
        nfound = 0
        for j in range(2, n):
            if i % j != 0:
                nfound = 1
                break
        if nfound == 0:
            if i == 0:
                i = 1
            return i
    return None

def solution(n: int = 100) -> int:
    """
    Returns the difference between the sum of the squares of the first n
    natural numbers and the square of the sum.

    >>> solution(10)
    2640
    >>> solution(15)
    13160
    >>> solution(20)
    41230
    >>> solution(50)
    1582700
    """

    sum_of_squares = 0
    sum_of_ints = 0
    for i in range(1, n + 1):
        sum_of_squares += i**2
        sum_of_ints += i
    return sum_of_ints**2 - sum_of_squares

def solution(nth: int = 10001) -> int:
    """
    Returns the n-th prime number.

    >>> solution(6)
    13
    >>> solution(1)
    2
    >>> solution(3)
    5
    >>> solution(20)
    71
    >>> solution(50)
    229
    >>> solution(100)
    541
    """

    count = 0
    number = 1
    while count != nth and number < 3:
        number += 1
        if is_prime(number):
            count += 1
    while count != nth:
        number += 2
        if is_prime(number):
            count += 1
    return number