For any positive integer $n$,the last digit of $5^n$ is always . . . . . . .

The decimal expansion of $\frac{2517}{6250}$ will terminate after how many decimal places?

If $n$ is an odd integer,then show that $n^{2}-1$ is divisible by $8$.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{29}{343}$.

Prove that one of any three consecutive positive integers must be divisible by $3$.

According to Euclid's division lemma,for given positive integers $a$ and $7$,there exist unique non-negative integers $q$ and $r$ such that $a = 7q + r$; where..........