Question

Please solve this problem with Python Language.

P#2. A Pythagorean triplet is a set of three natural numbers, a < b < c, for which a2 + b2 = c2 . For example, 32 + 42 = 52. And a + b + c = 3 + 4 + 5 = 12. There exists exactly two Pythagorean triplet for which a + b + c = 300. Find a, b, c.

Hints: Level-0 Algorithm:

1. Find the possible ranges of a and b for which a+b+c is around 300 (include the paper & pencil analysis at the end of your report)

2. Compute c for each combination of a and b

3. Verify if ?+?+?=300 and ?2+?2=?2 and ?<?<?

4. Print results

I really don't understand to do this problem.

Answer 1

PROGRAM:
import math


def pythagorean_triplet(n):     #defining function to find all possible triplet
    for b in range(2,n):        #starting value of b with 2 
        for a in range(1, b):   #staring value of a with 1 so a<b
            c = math.sqrt(a * a + b * b)   #find the value of c=(a^2+b^2)^(1/2)
            if c % 1 == 0 and a+b+c==n and a<b<c:  #verify three conditions 
                print(a, b, int(c))


pythagorean_triplet(300)

PROGRAM SCREENSHOT:


OUTPUT OF PROGRAM: