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 …

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 …

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 …

In this paper we study equation $$(x-dr)^ 5+\cdots+ x^ 5+\cdots+ (x+ dr)^ 5= y^ p $$ under
the condition $\gcd (x, r)= 1$. We present a recipe for proving the non-existence of non-trivial …

Perfect powers in sum of three fifth powers - ScienceDirect Skip to main contentSkip to article
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Sažetak In this paper, using a deep result on the existence of primitive divisors of Lehmer
numbers due to Y. Bilu, G. Hanrot and PM Voutier, we first give an explicit formula for all …

A note on the Diophantine equation (x+1)3+(x+2)3+⋯+(2x)3=yn Page 1 Elem. Math. (Online
first) DOI 10.4171/EM/450 © 2021 Swiss Mathematical Society Elemente der Mathematik …

Japanese mathematician Seki Takakazu (1642-1708), published also posthumously, in
1712 (and thus 1 year before Bernoulli!), the formula for the sums of powers and the …

A note on the Diophantine equation $(x + 1)^{3} + (x + 2)^{3} + \cdots + (2x)^{3} = y^{n}$ Page 1
Elemente der Mathematik 77 (2022), 142–143 DOI 10.4171/EM/450 © 2021 Swiss …