Euler Problem 9 : Special Pythagorean Triple

Euler Problem 9 Definition

Euler Problem 9: Pythagorean Triples

Scatter plot of the legs (a,b) of the first Pythagorean triples with a and b less than 6000. Negative values are included to illustrate the parabolic patterns. By Dearjean13Own work, CC BY-SA 4.0, Link

A Pythagorean triple is a set of three natural numbers, a < b < c , for which, a^2 + b^2 = c^2 . For example:

3^2 + 4^2 = 9 + 16 = 25 = 5^2 .

There exists exactly one Pythagorean triplet for which a + b + c = 1000 .

Find the product of a, b and c.

Brute Force Solution

This solution uses brute force and checks all combinations of a, b and c. To limit the solution space I used the fact that a < b < c, which implies that a < s/3,  and a < b < s/2, where s is the sum of the three sides.

a <- 0
b <- 0
c <- 0
s <- 1000
found <- FALSE
for (a in 1:floor((s/3))) {
    for (b in a:(s/2)) {
        c <- s - a - b
        if (a^2 + b^2 == c^2) {
            found <- TRUE
            break
        }
    }
    if (found) 
        break
}
answer <- a * b * c