On the Diophantine equation \((x-1)^k+x^k+(x+1)^k=y^n\)
In the paper the title equation is solved for the values \(k=2,3,4\). In the proofs, the author uses results on generalized Ramanujan-Nagell equations, and applies the theory of modular forms for certain ternary equations.
scientific article; zbMATH DE number 6330572