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How to demonstrate that   59 | 3n+3 + 2n+5 * 31n   ?

 

Thank you

 Dec 21, 2022
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3^(n + 3) = 3^n * 3^3

2^(n + 5) = 2^n * 2^5.

So our equation is 3^n * 3^3 + 2^n * 2^5 * 31^n.

27(3^n) + 32(2^n) * 31^n

Note that 59 = 32 + 27

Also, 27(3^n) will always be divisible by 27, and 32(2^n) * 31^n will also always be divisible by 32. 

Not saying that the sum will be divisible by 59, but good luck from here!

 Dec 22, 2022

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