# Question: let n p1p2prpr1pr2prs with r 1 and s 1...

###### Question details

Let N =
p_{1}p_{2}...p_{r}+p_{r+1}p_{r+2}...p_{r+s}
with r
1 and s
1 and where the p_{i} are distinct primes. Show that
p_{i} (does not divide) N for 1
i
r+s and hence deduce again that there exist infinitely many
primes.