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In his 'Memoir on Elliptic Divisibility Sequences', Morgan Ward's definition of the said sequences has the remarkable feature that it does not become at all clear until deep into the paper that there exist nontrivial such sequences. Even then, Ward's proof of coherence of his definition relies on displaying a sequence of values of quotients of Weierstraß(More)
In memory of Alf van der Poorten ABSTRACT. In 1987, Gordon gave an integer primality condition similar to the familiar test based on Fermat's little theorem, but based instead on the arithmetic of elliptic curves with complex multiplication. We prove the existence of infinitely many composite numbers simultaneously passing all elliptic curve primality tests(More)
It is well known that one can obtain explicit continued fraction expansions of e z for various interesting values of z ; but the details of appropriate constructions are not widely known. We provide a reminder of those methods and do that in a way that allows us to mention a number of techniques generally useful in dealing with continued fractions.(More)
We display a number with a surprising continued fraction expansion and show that we may explain that expansion as a specialisation of the continued fraction expansion of a formal series: A series c h X −h has a continued fraction expansion with partial quotients polynomials in X of positive degree (other, perhaps than the 0-th partial quotient). Simple(More)