Given solve the Diophantine equation:

.

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- August 12th 2007, 08:14 PM #1

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- August 13th 2007, 04:18 AM #2

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All permutations of for integers k and j are solutions. To see that these are the only solutions, rewrite as which, assuming , reduces to or with the other variable arbitrary, giving the solutions and, by symmetry in the original equation,

- August 24th 2007, 01:22 AM #3

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- August 24th 2007, 03:57 AM #4

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Apparently I can't post new threads, so I'll just append a problem here.

Source: The Art of Problem Solving (Vol 2)

Show that for any two positive numbers, RMS-AM >= GM-HM where RMS denotes the root-mean square, AM the arithmetic mean, GM the geometric mean, and HM the harmonic mean.

- August 24th 2007, 08:03 AM #5

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- August 24th 2007, 09:56 AM #6

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- August 29th 2007, 08:53 PM #7

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