A new conjecture on integer powers
We make a conjecture about integer powers which states that for any integer n > 2, the n th power of any arbitrary integer, including zero, can be expressed 'primitively' and 'non-trivially', in infinitely many different ways as the sum or difference of (n + 1) number of other...
Elmentve itt :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2015
|
| Sorozat: | Acta scientiarum mathematicarum
81 No. 3-4 |
| Kulcsszavak: | Számelmélet, Matematika |
| Tárgyszavak: | |
| mtmt: | http://dx.doi.org/10.14232/actasm-013-319-2 |
| Online Access: | http://acta.bibl.u-szeged.hu/36415 |
| Tartalmi kivonat: | We make a conjecture about integer powers which states that for any integer n > 2, the n th power of any arbitrary integer, including zero, can be expressed 'primitively' and 'non-trivially', in infinitely many different ways as the sum or difference of (n + 1) number of other non-zero, but not necessarily distinct integral n th powers. The conjecture is established for squares, cubes (partly) and biquadrates, and is open for the remaining cases. Finally, a few more questions are raised for further investigation. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 425-430 |
| ISSN: | 0001-6969 |