Wiki entry; Bezout's Identity

Hi everyone,
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> I added an entry in Wikipedia under the title "Bezout's Identity". I thought this was needed because it gives a precise method for deducing approximate ratios that is much more efficient than trying to guess the mediants from the outset. For eg, if we wish to know all the ratios that approximate a major third 81/64, we can easily obtain this by taking the mediants from 5/4 and 19/15 as our starting points (As Graham pointed out). But the problem with this is that we have to know what these numbers are in advance. This is all very well when we are dealing with well-known intervals like the major third here, but it becomes more a matter of guesswork when we choose random numbers (and math people like 'proofs'). By solving Bezout's Identity with input values such as 81 and 64, these numbers (-15, 19) are given directly as output values, while the second pair of numbers (4, 5) are the remainders. Someone might like to add onto what I've started, perhaps giving some reference to Erv Wilson and his work with mediant trees.
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> -Rick
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