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Help me please on my RSM homework!

The questions are:

(^ = to the power)

1. 36^5 - 6^9 is divisible by 30

2. 5^18 - 25^8 is divisible by 120

Thanks very much!

Respuesta :

LammettHash

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.