Here are 3 problems that i couldn't solve them. I would wonder if anybody help me.

a) If $\displaystyle 5|3a+4b$ prove that $\displaystyle 25|2a^2-3ab+2b^2$

b) If $\displaystyle a^9|b^5$ prove that $\displaystyle a^7|b^4$

c) If $\displaystyle a, b, c$ are natural numbers and $\displaystyle a^b|b^a$ and $\displaystyle b^c|c^b$, prove that $\displaystyle a^c|c^a$