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Author: MordredGit

pythagoreanTriplets.py

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+import math
+
+allPythagoreanTriplets = []
+
+def findPythagoreanTriplets(limit):
+    c,m = 0,2
+    global allPythagoreanTriplets
+
+    while c < limit:
+        for n in range(1, m):
+            a = m**2 - n**2
+            b = 2*m*n
+            c = m**2 + n**2
+            allPythagoreanTriplets.append([a,b,c])
+            if a + b + c == limit:
+                return [a, b, c]
+
+        m += 1
+
+
+product = 1
+for i in findPythagoreanTriplets(1000):
+    product *= i
+
+print(product)

smallestMultiple.py

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+import math
+import copy
+
+# A function to print all prime factors of
+# a given number n
+def primeFactors(n):
+    allPrimeFactors = [1]
+    temp = n
+    # Print the number of two's that divide n
+    while n % 2 == 0:
+        allPrimeFactors.append(2)
+        n = n // 2
+
+    # n must be odd at this point
+    # so a skip of 2 ( i = i + 2) can be used
+    for i in range(3,n+1,2):
+
+        # while i divides n , print i ad divide n
+        while n % i== 0:
+            allPrimeFactors.append(i)
+            n = n // i
+
+    # Condition if n is a prime
+    if len(allPrimeFactors) == 1:
+        allPrimeFactors.append(temp)
+    # number greater than 2
+    return allPrimeFactors
+
+
+# print(primeFactors(17))
+def smallestMultiple(n):
+    factors = []
+    for i in range(3, n+1):
+        temp = copy.deepcopy(factors)
+        currfactors = primeFactors(i)
+        print(currfactors)
+        print(temp)
+        for i in currfactors:
+            if i in temp:
+                print(i)
+                temp.remove(i)
+                currfactors.remove(i)
+
+        for i in currfactors:
+            factors.append(i)
+
+    return factors
+
+
+print(smallestMultiple(10))

sums.py

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+def sumOfSquares(n):
+    return n*(n+1)*(2*n+1)/6
+
+
+def squareOfSum(n):
+    return pow(n*(n+1)/2,2)
+
+
+print(squareOfSum(100) - sumOfSquares(100))

triangularNumber.py

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+import math
+
+# A function to print all prime factors of
+# a given number n
+def primeFactors(n):
+
+	# Print the number of two's that divide n
+	while n % 2 == 0:
+		print(2),
+		n = n // 2
+
+	# n must be odd at this point
+	# so a skip of 2 ( i = i + 2) can be used
+	for i in range(3,int(math.sqrt(n))+1,2):
+
+		# while i divides n , print i ad divide n
+		while n % i == 0:
+			print(i),
+			n = n // i
+
+	# Condition if n is a prime
+	# number greater than 2
+	if n > 2:
+		print(n)
+
+# Driver Program to test above function
+
+n = 6
+primeFactors(n)
+
+# This code is contributed by Harshit Agrawal