The Diophantine equation $Dx²+2^{2m+1}=yⁿ$

J. H. E. Cohn. "The Diophantine equation $Dx² + 2^{2m+1} = yⁿ$." Colloquium Mathematicae 98.2 (2003): 147-154. <http://eudml.org/doc/284865>.

@article{J2003,
abstract = {It is shown that for a given squarefree positive integer D, the equation of the title has no solutions in integers x > 0, m > 0, n ≥ 3 and y odd, nor unless D ≡ 14 (mod 16) in integers x > 0, m = 0, n ≥ 3, y > 0, provided in each case that n does not divide the class number of the imaginary quadratic field containing √(-2D), except for a small number of (stated) exceptions.},
author = {J. H. E. Cohn},
journal = {Colloquium Mathematicae},
keywords = {exponential Diophantine equation},
language = {eng},
number = {2},
pages = {147-154},
title = {The Diophantine equation $Dx² + 2^\{2m+1\} = yⁿ$},
url = {http://eudml.org/doc/284865},
volume = {98},
year = {2003},
}

TY - JOUR
AU - J. H. E. Cohn
TI - The Diophantine equation $Dx² + 2^{2m+1} = yⁿ$
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 2
SP - 147
EP - 154
AB - It is shown that for a given squarefree positive integer D, the equation of the title has no solutions in integers x > 0, m > 0, n ≥ 3 and y odd, nor unless D ≡ 14 (mod 16) in integers x > 0, m = 0, n ≥ 3, y > 0, provided in each case that n does not divide the class number of the imaginary quadratic field containing √(-2D), except for a small number of (stated) exceptions.
LA - eng
KW - exponential Diophantine equation
UR - http://eudml.org/doc/284865
ER -