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pro vyhledávání: '"R. G. E. Pinch"'
Autor:
R. G. E. Pinch
Publikováno v:
Mathematics of Computation. 60:841-845
The sequence of consecutive integer squares has constant second difference 2. We list every such sequence of squares containing a term less than 1000 2 {1000^2} .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e9c720bf7bf139872a89650746388df7
https://doi.org/10.1090/s0025-5718-1993-1181330-x
https://doi.org/10.1090/s0025-5718-1993-1181330-x
Autor:
R. G. E. Pinch
Publikováno v:
Mathematics of Computation. 61:381
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4de5e047b25809b95a372427d9a90073
https://doi.org/10.2307/2152963
https://doi.org/10.2307/2152963
Publikováno v:
The American Mathematical Monthly. 97:240
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::473b20e62575f7a79a0fb00aa0ff67c3
https://doi.org/10.2307/2324696
https://doi.org/10.2307/2324696
Autor:
R. G. E. Pinch
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 96:25-38
In this paper we list the elliptic curves defined over Q √ − 1, Q√ −2 or Q√ − 3 which have good reduction away from 2. The possible invariants of such curves are given in Table 1, and their minimal equations in Tables 2, 3 and 4. These ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eeae9f91f0d60c569d55f3ba0ed489f6
https://doi.org/10.1017/s0305004100061909
https://doi.org/10.1017/s0305004100061909
Autor:
R. G. E. Pinch
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 103:35-46
In this paper we describe a method for finding integer solutions of simultaneous Pellian equations, that is, integer triples (x,y,z) satisfying equations of the formwhere the coefficientsa,b,c,d,fare integers and we assume thata,c, andacare not squar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::62077ca4a97bba9683f0302155d4935c
https://doi.org/10.1017/s0305004100064598
https://doi.org/10.1017/s0305004100064598
Autor:
R. G. E. Pinch
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 97:63-68
For a ε R, we define a subset V of Rn to be a-convex if x, y ε V impliesClearly V is (1 — a)-convex iff it is a-convex: V is convex iff it is a-convex for all a ε [0, 1], and any set is 1-convex. We define the a-convex hull of V to be the inters
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::87b439eb967422b2900419c235d32e2f
https://doi.org/10.1017/s0305004100062587
https://doi.org/10.1017/s0305004100062587
Autor:
R. G. E. Pinch
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 100:435-457
In this paper we continue the study of elliptic curves defined over a quadratic field with good reduction at primes not dividing 2 begun in [9] (referred to as I). We extend the results of I to show that such a curve must have a point of order 2 also
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0cff86328694cc37bd4383f244fcc6fb
https://doi.org/10.1017/s0305004100066196
https://doi.org/10.1017/s0305004100066196
Autor:
R. G. E. Pinch
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 99:19-22
Bollobás and Erdös[1] have posed the problem:If a is irrational, show that for 1 ≤ i < j ≤ p the number of integers t with 1 ≤ t ≤ p such that {(t–i)2a} < d and {(t–j)2a} < d, 0 < d < 1, is d2p + o(p) uniformly in i, j.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::01c7b09e9d0c9eea6f04146475cf8023
https://doi.org/10.1017/s0305004100063878
https://doi.org/10.1017/s0305004100063878