Respuesta :

when n = 1 ,   5^n - 2  = 3     Divisible by 3

n = 2,   5^2 - 2   = 23 (not divisible by 3)
n = 3     5^3 - 2  =  123 ( divisible by 3)
n =4      5^4 -2   =  623 (not divisible)
n = 5     5^5 - 2 =  3123 (divisible)
n = 6    5^6 - 2 =  15623 (not divisible)

Looks like 5^n - 2 is divisible by 3 only if n is  odd.

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