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::::'''I assume you agree that Dickson's equations produce all the primitives. This is true when ''s'' and ''t'' are coprime as in line 1 below. (If they were not coprime, then we could remove common factor ''k'' as in the equation on line 2). But if instead we apply common factor ''k'' to our primitive triple(s) [ ''x, y, z''], we get the non-primitive triple(s) ['' x', y', z'''] as in line 3 where ''r', s', t' '' share a common factor ''k'' > 1. '''
:::::<math>\begin{align}
& x=\text{ }(r+s),\text{ }y=(r+t),\text{ }z=(r+s+t) \\
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\end{align}</math>
::::'''Thus given an arbitrary primitive [ ''x, y, z''] with ''s'','' t'' coprime, we get all of its multiples too. The latter have the form ['' x', y', z' '' ] where ''r', s', t''' share common factor ''k'' > 1.'''
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