igorvanloo

# These are the fifth power digit sum numbers except the last one is missing
#[4150, 4151, 54748, 92727, 93084] 

def sum_digits_mod(x):
    totalsum = 0
    while x != 0:
        totalsum += (x % 10)**5
        x = x // 10
    return totalsum
    

igorvanloo

def Divisors(x):
    divisors = []
    for i in range(1,int(math.sqrt(x))+1):
        if x % i == 0:
            divisors.append(i)
            if i != int(x/i):
                divisors.append(int(x/i))
    divisors.remove(x)
    return sum(set(divisors))

igorvanloo

def ppt(limit):
    triples = []
    for m in range(2,int(math.sqrt(limit))+1):
        for n in range(1,m):
            if (m+n) % 2 == 1 and math.gcd(m,n) == 1:
                a = m**2 + n**2
                b = m**2 - n**2
                c = 2*m*n
             
                p = max(a,b,c)

igorvanloo

def Partition(goal, alist):
    ways = [0] + [1] * (goal)
    for options in alist:
        for i in range(len(ways) - options):
            ways[i + options] += ways[i]
    return ways[-1] #-1 here if you don't want to include 4 + 0 as a partition of 4 for example

igorvanloo

def continued_fraction(x):
    m0 = 0
    d0 = 1
    a0 = math.floor(math.sqrt(x)) #These are the starting values
    temp_list = [a0]
    while True:
        mn = int(d0*a0 - m0) 
        dn = int((x - mn**2)/d0)
        an = int(math.floor((math.sqrt(x) + mn) / dn)) #new values
        temp_list.append(an)

igorvanloo

def Divisors(x): 
    divisors = []
    for i in range(1, int(math.sqrt(x)) + 1):
        if x % i == 0:
            divisors.append(i)
            divisors.append(int(x/i))
    divisors.remove(x) #Remove this line if you want to include x as a divisor of x
    return (divisors)

igorvanloo

#x % 10 will be the first digit, then we x // 10 to remove it and repeat

def sum_digits(x):
    totalsum = 0
    while x != 0:
        totalsum += x % 10
        x = x // 10
    return totalsum

igorvanloo

def numberToBase(n, b):
    if n == 0:
        return [0]
    digits = []
    while n != 0:
        digits.append(int(n % b))
        n //= b
    return digits[::-1]

igorvanloo

def fibonnaci(n): #Finds the nth fibonnaci number
    v1, v2, v3 = 1, 1, 0    # initialise a matrix [[1,1],[1,0]]
    for rec in bin(n)[3:]:  # perform fast exponentiation of the matrix (quickly raise it to the nth power)
        calc = v2*v2
        v1, v2, v3 = v1*v1+calc, (v1+v3)*v2, calc+v3*v3
        if rec=='1':
            v1, v2, v3 = v1+v2, v1, v2  
    return v2

igorvanloo

def is_prime(x):
	if x <= 1:
		return False
	elif x <= 3:
		return True
	elif x % 2 == 0:
		return False
	else:
		for i in range(3, int(math.sqrt(x)) + 1, 2):
			if x % i == 0: