I was able to come up with the integer solution that they also have in the textbook using the same method they used but I am really puzzled how they come up with a solution for all the possible integer combinations...how do they come up with that notation/equation that represents all the integer solutions ? I am talking about the very last line.
General solution using Euclidean Algorithm
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$\begingroup$
algebra-precalculus
discrete-mathematics
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0This illustrates the applicability of Number Theory to real life. Not. – 2012-02-12
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0@AndréNicolas Your Comment illustrates the applicability of [Borat](http://en.wikipedia.org/wiki/Borat) to the daily life. :P – 2012-02-12
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0@user21436 Very amusing! – 2017-12-10