$(i)$ Prove that If $3|(7n-5)$, then $9|(28n^2+13n-5)$.
$(ii)$ If $a$ is an integer not divisible by $2$ or $3$ , then $24|(a^2+23)$.
$(iii)$ If $a$ is an arbitrary integer, then $360|a^2(a^2-1)(a^2-4)$.
$(iv)$ Show that $289\nmid (a^2-3a-19)$ for all integer $a$.
ช่วยหน่อยครับ
