We investigate conditions which ensure that systems of binomial polynomials with integer coefficients are simultaneously free of large prime factors. In particular, for each positive number epsilon, we show that there are infinitely many strings of consecutive integers of size about n, free of prime factors exceeding n(epsilon), with the length of the strings tending to infinity with speed log log log log n.
|Number of pages||11|
|Journal||Journal of the Australian Mathematical Society Series A: Pure Mathematics and Statistics|
|Publication status||Published - Apr 1998|
- smooth numbers
- consecutive integers