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Euler's conjecture
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(Conjecture)
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In 1769, Leonhard Euler conjectured that for $1 < k < n$ there is no set of positive integers $a_1, \ldots, a_k$ such that $$\sum_{i = 1}^k {a_i}^n = m^n,$$ where $m$ is an integer. Lander and Parkin in 1966 disproved the conjecture with this $k = 4, n = 5$ counterexample: $27^5 + 84^5 + 110^5 + 133^5 = 144^5$ More counterexamples have been
discovered since then.
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"Euler's conjecture" is owned by PrimeFan. [ owner history (1) ]
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(view preamble | get metadata)
| Other names: |
Euler conjecture |
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Cross-references: counterexample, conjecture, integers, positive, Euler
There is 1 reference to this entry.
This is version 4 of Euler's conjecture, born on 2006-11-22, modified 2006-11-24.
Object id is 8580, canonical name is EulersConjecture.
Accessed 2048 times total.
Classification:
| AMS MSC: | 11B13 (Number theory :: Sequences and sets :: Additive bases) | | | 11D41 (Number theory :: Diophantine equations :: Higher degree equations; Fermat's equation) |
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Pending Errata and Addenda
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