Given solve the Diophantine equation:

.

Results 1 to 7 of 7

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

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

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

- Joined
- Jun 2007
- Posts
- 18

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

- Joined
- Jan 2006
- From
- Gdansk, Poland
- Posts
- 117

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

- Joined
- Jun 2007
- Posts
- 18

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

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

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

- Joined
- Jan 2006
- From
- Gdansk, Poland
- Posts
- 117

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

- Joined
- Oct 2005
- From
- Earth
- Posts
- 1,599