On the Exponential Diophantine Equation (m(2) + m+1)(x) + m(y) = (m+1)(z)


ALAN M.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.17, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 17 Konu: 6
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00009-020-01613-4
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS

Özet

Let m >= 1 be a positive integer. We show that the exponential Diophantine equation (m(2) + m + 1)(x) + m(y) = (m + 1)(z) has no positive integer solutions other than (x, y, z) = (1, 1, 2) when m is not an element of {1, 2, 3}.