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On powerful numbers.

Mollin, R.A., Walsh, P.G. (1986)

International Journal of Mathematics and Mathematical Sciences

On second 2-descent and non-congruent numbers

Yi Ouyang, Shenxing Zhang (2015)

Acta Arithmetica

We use the so-called second 2-descent method to find several series of non-congruent numbers. We consider three different 2-isogenies of the congruent elliptic curves and their duals, and find a necessary condition to estimate the size of the images of the 2-Selmer groups in the Selmer groups of the isogeny.

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