# May be this Conjecture is hold? with $n$ consecutive postive integers problem

Somedays a ago,when discussed famous problem ($k$ consecutive postive intgers is never a square) with a math teacher,at last,We get the following questions( if we solve following problem,then I think the famous problem have other simple methods to solve it)

Conjecture: for any set $S$ of $n(≥4)$ consecutive positive integers there are two distinct $x,y\in S$ such that pp does not divide $x$ and pp does not divide $y$ where $p(<n)$ is an odd prime?

• Title is badly worded and unhelpful. The post itself needs improvement in grammar and sentence construction. In the current form it is unclear what the hypothesis is and what is to be proved. – P Vanchinathan Jan 22 '16 at 5:55
• The conjecture as currently written is not clear. Do you mean: for any set $S$ of $n(\ge4)$ consecutive positive integers there are two distinct $x,y\in S$ such that $p$ does not divide $x$ and $p$ does not divide $y$ where $p(<n)$ is an odd prime? – Frentos Jan 23 '16 at 0:35
• @Frentos,Yes,Thanks – math110 Jan 23 '16 at 4:10