scholarly journals Series involving the least and the greatest prime factor of a natural number

2010 ◽  
pp. 197-201
Author(s):  
Gabriel Mititica ◽  
Laurenţiu Panaitopol
Keyword(s):  
Natural Number ◽  
Prime Factor ◽  
Greatest Prime Factor

scholarly journals Sommes friables d'exponentielles et applications

2015 ◽  
Vol 67 (3) ◽  
pp. 597-638 ◽  
Author(s):  
Sary Drappeau
Keyword(s):  
Asymptotic Formula ◽  
Saddle Point ◽  
Exponential Sums ◽  
Prime Factor ◽  
Character Sums ◽  
Contour Integration ◽  
Point Method ◽  
Saddle Point Method ◽  
Greatest Prime Factor

AbstractAn integer is said to be y–friable if its greatest prime factor is less than y. In this paper, we obtain estimates for exponential sums over y–friable numbers up to x which are non–trivial when y ≥ . As a consequence, we obtain an asymptotic formula for the number of y-friable solutions to the equation a + b = c which is valid unconditionally under the same assumption. We use a contour integration argument based on the saddle point method, as developped in the context of friable numbers by Hildebrand and Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers.

scholarly journals On the greatest prime factor of $(ax^m + by^n)$

1980 ◽  
Vol 36 (1) ◽  
pp. 21-25 ◽  
Author(s):  
T. Shorey
Keyword(s):  
Prime Factor ◽  
Greatest Prime Factor

Perfect powers in values of certain polynomials at integer points

1986 ◽  
Vol 99 (2) ◽  
pp. 195-207 ◽  
Author(s):  
T. N. Shorey
Keyword(s):  
Prime Factor ◽  
Integer Points ◽  
Greatest Prime Factor ◽  
Image Position

1. For an integer v > 1, we define P(v) to be the greatest prime factor of v and we write P(1) = 1. Let m ≥ 0 and k ≥ 2 be integers. Let d1, …, dt with t ≥ 2 be distinct integers in the interval [1, k]. For integers l ≥ 2, y > 0 and b > 0 with P(b) ≤ k, we consider the equationPutso that ½ < vt ≤ ¾. If α > 1 and kα < m ≤ kl, then equation (1) implies thatfor 1 ≤ i ≤ t and hence

scholarly journals On the greatest prime factor of $n^2+1$

1982 ◽  
Vol 32 (4) ◽  
pp. 1-11 ◽  
Author(s):  
Jean-Marc Deshouillers ◽  
Henryk Iwaniec
Keyword(s):  
Prime Factor ◽  
Greatest Prime Factor
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