2013-04-10 23:57:08 -07:00
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N= 100;
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a = 1:N;
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b = a(ones(N,1),:).^2;
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b = b+b';
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b = sqrt(b); [y,x]=find(b==fix(b)); % test
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% here some alternative tests
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% b = b.^(1/k); [y,x]=find(b==fix(b)); % test 2
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% [y,x]=find(b==(fix(b.^(1/k)).^k)); % test 3
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% b=b.^(1/k); [y,x]=find(abs(b - round(b)) <= 4*eps*b);
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z = sqrt(x.^2+y.^2);
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ix = (z+x+y<100) & (x < y) & (y < z);
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2014-01-17 05:32:22 +00:00
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p = find(gcd(x(ix),y(ix))==1); % find primitive triples
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2013-04-10 23:57:08 -07:00
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printf('There are %i Pythagorean Triples and %i primitive triples with a perimeter smaller than %i.\n',...
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sum(ix), length(p), N);
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