This question states:
A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
I'm not sure what's it trying to ask you. Are we trying to find a2 + b2 = c2 and then plug those numbers into a + b + c = 1000?
You need to find the a, b, and c such that both a2 + b2 = c2 and a + b + c = 1000. Then you need to output the product a * b * c.
Like a large number of project euler problems, it's all about finding a set of numbers that simultaneously fulfil multiple constraints.
In this case, the constraints are:
1) a^2 + b^2 = c^2
2) a+b+c = 1000
In the early questions the solution can be as simple as nested loops which try each possible combination.
These problems are often solvable trivially, if you find the proper insight. The trick here is to use a little algebra before you ever write a loop. I'll give you one hint. Look at the formula to generate pythagorean triples. Can you write the sum of the side lengths in a useful way?