Note on a Question by S. Bagchi and B. Bagchi
نویسنده
چکیده
In [l] Bagchi and Bagchi conjectured that one of the hypotheses of their theorem 2(d) is superfluous. This turns out to be true: PROPOSITION. Let 4 = 9 mod 16 be a prime power such that 2 is a fourth power in Fq. Then 1 f fi are nonsquares in Fp. Pruc$ Let p be a primitive eighth root of unity in Fq (note that /3 is a nonsquare). Because of (02 + 1)2 = p4 + 202 + 1 = 202 we obtain that (0 * + 1)/p is a root of 2 which we denote by fi. Note that fi is a square and therefore p* + 1 is a nonsquare. Thus the equation (1 + Q/3@* + 1) = (02 + p + l)@ + 1) = p(1 + p)* shows that 1 + fi is a nonsquare in Fq. Since (1 + @(l fi) = -1 this is also true for 1 4%.
منابع مشابه
Book Review: “Bagchi D., Swaroop A. (2017). Food Toxicology. CRC Press, Boca Raton. ISBN: 978-1-4987-0874-6”
This article has no abstract.
متن کاملThe Effect of Red Background Color on Willingness-to-Pay: The Moderating Role of Selling Mechanism
متن کامل
Homogeneous operators and projective representations of the Möbius group: A survey
This paper surveys the existing literature on homogeneous operators and their relationships with projective representations ofPSL(2,R) and other Lie groups. It also includes a list of open problems in this area.
متن کامل1 9 D ec 1 99 6 GRAPH - BASED LOGIC AND SKETCHES II : FINITE - PRODUCT CATEGORIES AND EQUATIONAL LOGIC ( PRELIMINARY REPORT )
In [Wells, 1990] the second author introduced the notion of form, a graph-based method of specification of mathematical structures that generalizes Ehresmann’s sketches. In [Bagchi and Wells, 1996], the authors produced a structure for forms which provides a uniform proof theory based on finite-limit constructions for many types of forms, including all types of sketches and also forms that can ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Des. Codes Cryptography
دوره 2 شماره
صفحات -
تاریخ انتشار 1992