On the greatest prime Factor of a polynomial
نویسندگان
چکیده
منابع مشابه
On the greatest prime factor of integers
Let N be a positive integer and let A and B be dense subsets of {1, . . . , N}. The purpose of this paper is to establish a good lower bound for the greatest prime factor of ab+ 1 as a and b run over the elements of A and B respectively. 1991 AMS Mathematics Subject Classification. Primary 11N30, Secondary 11L05, keywords: greatest prime factor, Selberg’s sieve, Kloosterman sums.
متن کاملON THE GREATEST PRIME FACTOR OF (ab+ 1)(ac+ 1)
We prove that for integers a > b > c > 0, the greatest prime factor of (ab+1)(ac+1) tends to infinity with a. In particular, this settles a conjecture raised by Györy, Sarkozy and Stewart, predicting the same conclusion for the product (ab + 1)(ac + 1)(bc + 1). In the paper [GSS], Gÿory, Sarkozy and Stewart conjectured that, for positive integers a > b > c, the greatest prime factor of the prod...
متن کاملON THE GREATEST PRIME FACTOR OF ab + 1
We prove that whenever A and B are dense enough subsets of {1, . . . , N}, there exist a ∈ A and b ∈ B such that the greatest prime factor of ab + 1 is at least N1+|A|/(9N).
متن کاملOn the Greatest Prime Factor of Some Divisibility Sequences
Let P (m) denote the greatest prime factor of m. For integer a > 1, M. Ram Murty and S. Wong proved that, under the assumption of the ABC conjecture, P (a − 1) ,a n2− for any > 0. We study analogues results for the corresponding divisibility sequence over the function field Fq(t) and for some divisibility sequences associated to elliptic curves over the rational field Q. In honor of M. Ram Murt...
متن کاملOn the Greatest Prime Divisor of Np
Let E be an elliptic curve defined over Q. For any prime p of good reduction, let Ep be the reduction of E mod p. Denote by Np the cardinality of Ep(Fp), where Fp is the finite field of p elements. Let P (Np) be the greatest prime divisor of Np. We prove that if E has CM then for all but o(x/ log x) of primes p ≤ x, P (Np) > p, where θ(p) is any function of p such that θ(p)→ 0 as p→∞. Moreover ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1969
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500012967