Project Euler

Problem 9: Pythagorean Triplet

A Pythagorean triplet 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 \(abc\).

Let’s solve this using Julia

Code

sum = 1000
a = 0
b = 0
c = 0

for i = 1:sum
    for j = 1:sum
        for k = 1:sum
            if (1000 == i + j + k) & (i^2 + j^2 == k^2) 
                a = i
                b = j 
                c = k
            end
        end
    end
end

println("a = ", a)
println("b = ", b)
println("c = ", c)
println(" ")
println("a + b + c = ", a + b + c)
println("a^2 + b^2 = ", a^2 + b^2)
println("c^2 = ", c^2)
println(" ")
println("a*b*c = ", a*b*c)

a = 375
b = 200
c = 425
 
a + b + c = 1000
a^2 + b^2 = 180625
c^2 = 180625
 
a*b*c = 31875000

Therefore we have that the product is 31,875,000.