Better documentation for project euler problems

Author: Jessica Yung

mathematics/project-euler/1-multiples-of-three-and-five.py

@@ -1,6 +1,8 @@
 """
 Problem 1:
+
 Find the sum of all multiples of 3 or 5 below a positive integer n
+
 """
 
 # Function calculates sum of multiples of k less than n

mathematics/project-euler/2-even-fibonacci-numbers.py

@@ -1,6 +1,8 @@
 """
 Problem 2:
+
 Calculate the sum of all even Fibonacci numbers below positive integer n
+
 """
 
 # Function to calculate nth Fibonacci number, n being a non-negative integer.

mathematics/project-euler/3-largest-prime-factor.py

@@ -1,6 +1,8 @@
 """
 Problem 3: 
+
 Find the largest prime factor of a positive integer n
+
 """
 import math
 

mathematics/project-euler/4-largest-palindrome-product.py

@@ -0,0 +1,50 @@
+"""
+Problem 4:
+
+Find the largest palindrome made from the product of two 3-digit integers which is less than positive integer n.
+
+"""
+
+# Function to test if a number is a palindrome
+def is_palindrome(n):
+	is_palindrome = True
+	n = str(n)
+	for i in range(int(len(n)/2)):
+		if n[i] != n[len(n)-1-i]:
+			is_palindrome = False
+			break
+	return is_palindrome
+
+# Narrow range
+def largest_three_digit_to_consider(n):
+	k = 999
+	while k*100 > n:
+		k -= 1
+	return k
+
+"""
+Given the palindromic product must be a six-digit number, it must also be a multiple of 11. Thus at least one of the factors must be a multiple of 11.
+
+"""
+
+# Systematically go through all relevant products and find the greatest palindrome product
+def greatest_palindromic_product_below_n(n):
+	k = largest_three_digit_to_consider(n)
+	l = int(k/11)
+	greatest = 0
+	# Let a be the factor that must be a multiple of 11
+	for i in range(10, l+1):
+		a = 11*i
+		for j in range(100,k):
+			product = a*j
+			if product < n:
+				if product > greatest:
+					if is_palindrome(product):
+						greatest = product
+	return greatest
+
+# Read input and solve
+t = int(input().strip())
+for i in range(t):
+    n = int(input().strip())
+    print(greatest_palindromic_product_below_n(n))

mathematics/project-euler/5-smallest-multiple.py

@@ -0,0 +1,12 @@
+""" 
+Problem 5: 
+
+2520 is the smallest number that can be divided by each of the numbers from  to  without any remainder. 
+What is the smallest positive number that is evenly divisible(divisible with no remainder) by all of the numbers from 1 to N?
+
+"""
+
+# Find all the prime factors and their powers in that number
+# Idea: Recursive
+
+def blah():

mathematics/project-euler/6-sum-square-difference.py

@@ -0,0 +1,27 @@
+"""
+Problem 6:
+
+Find the absolute difference between the sum of the squares of the first n natural numbers and the square of the sum.
+
+"""
+
+# Need abs((1^2+2^2+...+N^2) - (1+2+...+N)^2)
+
+# Sum of the squares of the first n natural numbers
+def sum_of_squares(n):
+	sum = 0
+	for i in range(1,n+1):
+		sum += i**2
+	return sum
+
+def square_of_sum(n):
+	sum = 0
+	for i in range(1, n+1):
+		sum += i
+	return sum**2
+
+# Read input and solve
+t = int(input().strip())
+for i in range(t):
+	n = int(input().strip())
+	print(abs(sum_of_squares(n) - square_of_sum(n)))

mathematics/project-euler/7-nth-prime.py

@@ -0,0 +1,22 @@
+"""
+Problem 6:
+
+Find the nth prime number. 
+n=< 10**4
+
+"""
+
+primes=[]
+def all_primes_under_n(n):
+	primes_under_n = []
+	for i in range(n):
+		if isprime(i) == True:
+			primes_under_n.append(i)
+	return primes_under_n
+
+def nth_prime(n):
+	all_primes_under_n[n]
+
+	i = int(primes[n-2])
+	while 
+