New results regarding the full solution of the diophantine equation <mml:math alttext="$x^2 + 2^k = y^n" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math> in positive integers are obtained. These support a previous conjecture, without providing a complete proof.

The Diophantine equation <mml:math alttext="$x^2 + 2^k = y^n" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>, II

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International Journal of Mathematics and Mathematical Sciences

The Diophantine equation x2+2k=yn, II

Abstract

Copyright