We study the equation (x− 4 r) 3+(x− 3 r) 3+(x− 2 r) 3+(x− r) 3+ x 3+(x+ r) 3+(x+ 2 r) 3+(x+ 3 r)
3+(x+ 4 r) 3= yp, which is a natural continuation of previous works carried out by A. Argáez …

Perfect powers that are sums of squares in a three term arithmetic progression Page 1
International Journal of Number Theory Vol. 14, No. 10 (2018) 2729–2735 c World Scientific …

Using only elementary arguments, Cassels and Uchiyama (independently) determined all
squares that are sums of three consecutive cubes. Zhongfeng Zhang extended this result …

Research on power values of power sums has gained much attention of late, partially due to
the explosion of refinements in multiple advanced tools in (computational) number theory in …

Let $ k,\ell\geq2 $ be fixed integers and $ C $ be an effectively computable constant
depending only on $ k $ and $\ell $. In this paper, we prove that all solutions of the equation …

On perfect powers that are sums of cubes of a five term arithmetic progression - ScienceDirect Skip
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We prove that the equation (x− 3 r) 3+(x− 2 r) 3+(x− r) 3+ x 3+(x+ r) 3+(x+ 2 r) 3+(x+ 3 r) 3=
yp only has solutions which satisfy xy= 0 for 1≤ r≤ 10 6 and p≥ 5 prime. This article …

Perfect powers that are sums of squares of an arithmetic progression Page 1 ROCKY
MOUNTAIN JOURNAL OF MATHEMATICS Volume 51 (2021), No. 3, 933–949 DOI: 10.1216 …

Power Values of Power Sums: A Survey Page 167 Power Values of Power Sums: A Survey
Nirvana Coppola, Mar Curcó-Iranzo, Maleeha Khawaja, Vandita Patel, and Özge Ülkem Check …

Perfect powers in sum of three fifth powers - ScienceDirect Skip to main contentSkip to article
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