We show that the value of the (p−1)st Bernoulli polynomial at a/q can be given, mod p, in terms of a certain linear recurrence of order [q/2], which depends only on a,q and p \pmod q.
We prove Erdos's conjecture that \binom {2n}n is not squarefree for all n>4, by obtaining explicit upper bounds on exponential sums of the form
\sum_n \Lambda(n)e(x/n) for n\sim N\ll x^{3/5}
On the number of co-prime-free sets (with Neil Calkin)
Number Theory: New York Seminar 1991-1995, (D. Chudnovsky, G. Chudnovsky and M. Nathanson, eds) Springer-Verlag, 1996, 9-18.
We investigate the number of subsets of the integers up to x that have certain given arithmetic properties.