# Check what values of three variables fulfill a certain condition

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ABG on 1 Oct 2022
Commented: ABG on 1 Oct 2022
Hi guys! I'm stuck with a problem where if have to find all the values of x, y and z which fulfill the next equation: x^2+y^2=z^2.
I have tried it in many ways, but I can't get a result.
I don't know if you could help me..
Thank you very much!
x=[1:1:100]; % values of X
y=[1:1:100]; % values of Y
z=[1:1:100]; % values of Z
found=0;
for i=1: length(x)
for k=1:length(y)
for l=1: length(z)
if x.*x+y.*y==z.*z
found=1;
end
end
end
end
if found==1
disp(x,y,z)
end

Walter Roberson on 1 Oct 2022
You do not need to loop over z. Instead, take z = sqrt(x.^2+y.^2) and test to see whether z is an integer.
And... vectorize. For a given x value you can compute for a vector of y values, and use logical indexing to figure out which (if any) entries match.
I have implemented a fully vectorized version that uses no loops at all, and I have implemented a version that uses a single loop; both approaches work fine. I am not posting the code here because you are obviously working on an assignment.
ABG on 1 Oct 2022
Thanks for the answer Walter. Actually is not an assignment (is a preparatory course, I want to get into programming with matlab for my master's degree) and this part of the course is really important for me in order to understand it all.
Is it possible from you to post one of your versions please? As it will be easier for me to understand how to complete operate.
Thank you so much for your help!

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