Problem of the Week 1021

Erroneous Reduction, Usually

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Imagine you are an algebra teacher and a student claims that x/y = (2y + 1 - n)/(2x - 1 - n). Well, of course this cannot be true, but it turns out it is sometimes true. For which positive integers n is it true that there exist positive integers x and y making the equation true?

Source: College Math Journal Problem #750 by Angelo DiDomenica (Question vol. 34 no. 3, solution vol. 35 no. 2, but that would be cheating.)

© Copyright 2004 Stan Wagon. Reproduced with permission.