Given solve the Diophantine equation:
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,
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.