1. [tex]36^5-6^9=(6^2)^5-6^9=6^{10}-6^9=6^9(6-1)=6^9\cdot5[/tex]
Then with [tex]30=6\cdot5[/tex], it's easy to see the above is divisible by 30.
2. [tex]5^{18}-25^8=5^{18}-(5^2)^8=5^{18}-5^{16}=5^{16}(5^2-1)=5^{16}\cdot24[/tex]
[tex]120=5\cdot24[/tex] and the claim follows.
