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The equivalence may be read on the regular continued fraction representation, as shown by the following theorem of [[Joseph Alfred Serret|Serret]]:
'''Theorem''': Two irrational numbers ''x'' and ''y'' are equivalent if and only if there exist two positive integers ''h'' and ''k'' such that the regular [[continued fraction]] representations of ''x'' and ''y''
:<math>\begin{align}
x &= [u_0; u_1, u_2, \ldots]\, , \\
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