Exercise $1\mathrm{.}4.$ Use the idea of breaking the positive integers into three fam$-$

ilies according to their remainders when divided by $3$ to solve the following

problems:

$1.$ If m is divisible by $3,$ what are the $(3,$ m$)-$accessible positive integers?

$2.$ Find the $(3,5)-$accessible positive integers, the $(3,7)-$accessible positive

integers, and the $(3,8)-$accessible positive integers.

$3.$ Suppose m is a positive integer not divisible by $3.$ Using the preceding

examples, guess what the largest N might be such that N is $(3,$ m$)-$

inaccessible but every integer n $>$ N is $(3,$ m$)-$accessible.

$4.$ Make an argument showing that your guess is correct.