Prove that,if a positive integer is of the form $6m + 5$,then it is also of the form $3n + 2$ for some integer $n$.

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{77}{210}$

"The product of three consecutive positive integers is divisible by $6$". Is this statement true or false? Justify your answer.

The following real number is expressed in decimal form. Determine whether it is rational or not. If rational,express it in the form of $\frac{p}{q}$. $5 . \overline{123456}$

Prove that $n^{2}-n$ is divisible by $2$ for every positive integer $n$.

Find the square root of: $\frac{7}{4} + \sqrt{3}$