THESIS
2005
Abstract
In 2001, Stewart and Yu [1] proved that there exists effectively computable positive numbers c
1 and c
2 such that for all positive integers x, y and z satisfying x + y = z and (x,y,z)=1,
1 1/3 3 a 2 3 2 i 1 i i-1 x y z x y z 1 2 1 44 2...[ Read more ]In 2001, Stewart and Yu [1] proved that there exists effectively computable positive numbers c
1 and c
2 such that for all positive integers x, y and z satisfying x + y = z and (x,y,z)=1,
z
1G1/3(log G)3)
and (if z > 2 in addition)
za), a=c2log3G*/log2G
where G is the greatest square-free factor of xyz, G * = max(G,16), logi denotes the ith iterate of the logarithmic function with log1t = log t and logit = log(logi-1t ) for i = 2,3, . . . , and p' = min(px, py, pz) with px, py and pz being the greatest prime factor of x, y and z respectively.
In this paper, we will take G* = max(G, 9699690) due to technical convenience and will prove that we can take c1 and c2 as c1= exp(2.6 x 1044 ) and c2= 13.6 respectively.
[1] C. L. Stewart and Kunrui Yu, On the abc conjecture II. Duke Mathematical Journal. 108 No.1 (2001), 169-181.
Post a Comment