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JSC
2007
104views more  JSC 2007»
14 years 9 months ago
Summation algorithms for Stirling number identities
We consider a class of sequences defined by triangular recurrence equations. This class contains Stirling numbers and Eulerian numbers of both kinds, and hypergeometric multiples...
Manuel Kauers
ISSAC
2004
Springer
88views Mathematics» more  ISSAC 2004»
15 years 3 months ago
Non-liouvillian solutions for second order Linear ODEs
There exist sound literature and algorithms for computing Liouvillian solutions for the important problem of linear ODEs with rational coefficients. Taking as sample the 363 secon...
L. Chan, E. S. Cheb-Terrab
ISSAC
2009
Springer
172views Mathematics» more  ISSAC 2009»
15 years 4 months ago
Liouvillian solutions of irreducible linear difference equations
In this paper we give a new algorithm to compute Liouvillian solutions of linear difference equations. Compared to the prior algorithm by Hendriks and Singer, our main contributi...
Yongjae Cha, Mark van Hoeij
MOC
1998
147views more  MOC 1998»
14 years 9 months ago
On the Diophantine equation |axn - byn | = 1
If a, b and n are positive integers with b ≥ a and n ≥ 3, then the equation of the title possesses at most one solution in positive integers x and y, with the possible exceptio...
Michael A. Bennett, Benjamin M. M. de Weger
TCC
2007
Springer
170views Cryptology» more  TCC 2007»
15 years 3 months ago
Secure Linear Algebra Using Linearly Recurrent Sequences
In this work we present secure two-party protocols for various core problems in linear algebra. Our main result is a protocol to obliviously decide singularity of an encrypted matr...
Eike Kiltz, Payman Mohassel, Enav Weinreb, Matthew...