Show that there are arbitrarily long gaps between
square free integers. That is,if k is any positive integer,there
is a number N so that none of N + 1, N + 2, ..., N + k are
square free.
Show that there are arbitrarily long gaps between
square free integers. That is,if k is any positive integer,there
is a number N so that none of N + 1, N + 2, ..., N + k are
square free.
this claim is true only for $\displaystyle k=1,2,3.$ because if $\displaystyle k \geq 4,$ then for any $\displaystyle N$ at least one of the elements in $\displaystyle N + 1, N + 2, \cdots , N + k,$ will divide $\displaystyle 4$.