A note on the diophantine equation $(x^2-1)(y^2-1)=(z^2-1)^2$

Huaming Wu; Maohua Le

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Improving on some results of J.-L. Nicolas [], the elements of the set $𝒜 = 𝒜 (1 + z + z^{3} + z^{4} + z^{5})$ , for which the partition function $p (𝒜, n)$ (i.e. the number of partitions of $n$ with parts in $𝒜$ ) is even for all $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

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A local analogue of the Grothendieck Conjecture is an equivalence between the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p \neq 0$ and the category of absolute Galois groups of fields $K$ together with their ramification filtrations. The case of characteristic 0 fields $K$ was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case $p > 2$ (but with no restrictions on the characteristic of $K$ )....

Displaying similar documents to “A note on the diophantine equation ( x 2 - 1 ) ( y 2 - 1 ) = ( z 2 - 1 ) 2 ”

Displaying similar documents to “A note on the diophantine equation $(x^{2} - 1) (y^{2} - 1) = {(z^{2} - 1)}^{2}$ ”