24. Determine whether the following assertions are true or false. If true, prove the result, and if false, give a counterexample. (1) If $(a, b)=(a, os then $[a, b]=[a, c]$. (2) If $(a, b)=(a, os then $\left(a^{2), b^{2} ight)=\left(a^{2}, C^{2} ight)$. (3) If $(a, b)=(a, os then $(a, b)=(a, b, c)$. (4) If $ps'is a prime and Sp \mid a$ and p \mid\left(a^{2}+b^{2} ight) then $p \mid b$. (5) If $p is a prime and $p \mid a^{7}$ then $p \mid a$. CS.SD. 134