PLEASE DO NOT COPY PASTE FROM CHEGG/OTHERWISE I'LL REPORT YOU OR GIVE OU A DISLIKE

24. Determine whether the following assertions are true or false. If true, prove the result, and if false, give a counterexample. (1) If $(a, b)=(a, c)$ 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 $(a, b)=(a, c$ 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 $ps is a prime and sp \mid a^{7}$ then Sp \mid a$. (6) If $a^{3} \mid c^{3}$ then $a \mid c$. (7) If $a^{3} \mid c^{2}$ then sa \mid c$. (8) If $a^{2} \mid c^{3}$ then $a \mid c$. (9) If $ps is a prime and sp \mid\left(a^{2}+b^{2} ight) $ and $p \mid\left(b^{2}+c^{2} ights then $p \mid\left(a^{2}-C^{2} ight). (10) If $p$ is a prime and $p \mid\left(a^{2}+b^{2} ight) $ and $p \mid\left(b^{2}+c^{2} ight) $ then $p \mid\left(a^{2}+c^{2} ight)$.CS.SD. 170