Abstract
We make a conjecture about integer powers which states that for any integer n ≥ 2, the nth 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 nth 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.
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Acknowledgment
I was almost delayed by five months due to my critical health problems to write the revised version of the original paper in accordance with the comments of the referee. Hence, I apologize for this delay, and thank the referee for the comments which improved the presentation of the paper.
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Communicated by L. Zádori
This work was supported by my family.
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Jena, S.K. A new conjecture on integer powers. ActaSci.Math. 81, 425–430 (2015). https://doi.org/10.14232/actasm-013-319-2
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DOI: https://doi.org/10.14232/actasm-013-319-2