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Fifth powers (Posted on 2013-01-06) Difficulty: 3 of 5
Given that n5 = 1335 + 1105 + 845 + 275.
Find that value of n using only pen and paper.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts An interesting reference | Comment 2 of 8 |

http://www.ams.org/journals/mcom/1967-21-097/S0025-5718-1967-0220669-3/S0025-5718-1967-0220669-3.pdf

A Counterexample to Euler's Sum of Powers Conjecture By L. J. Lander and T. R. Parkin

"A search was conducted on the CDC 6600 computer for nontrivial solutions in nonnegative integers of the Diophantine equation....The fourth case was the unexpected result.
27^5+84^5 + 110^5 + 133^5 = 144^5
which is a counterexample to Euler's conjecture that at least k positive kth powers are required to sum to a kth power, except for the trivial case of one kth power: y^k = y^k . The search was again specialized to n = 4 over the range to 750, but no further primitive solutions exist in that range."

Edited on January 8, 2013, 11:50 am
  Posted by broll on 2013-01-06 23:30:32

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