Find a positive integer p such that: (p+1)(p+2)....(p+500)/500! is an integer with no prime factors less than 500.

(p+1)(p+2)...(p+500)/500! is the same as p+500 choose 500. Therefore, we need a number p such that p+500 choose 500 has no prime factors less than 500.

Posted by Math Man on 2011-11-19 23:01:33