Abstrak

Kembali

GivenR a set of integers, F1(X1,X2) a linear form and F2(X1,X2) an irreducible quadratic form, we study in this work the cardinality #{1 <= n1, n2 <= x : F1(n1, n2) ∈ R and P + (F2(n1, n2)) <= y}, where P + (n) denotes the greatest prime factor of an integer n. In particular, we give an asymptotic formula for the number of pairs of integers (n1, n2) in the square [1, x]2 such that F1(n1, n2) and F2(n1, n2) are both y-friable in the range exp  log x(log log log x)1+ε log log x  <= y <= x2.