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Sagot :
If the number is supposed to be
[tex]a^n + a^{n+1} + a^{n+2} + a^{n+3} + a^{n+4}[/tex]
then it can be factorized as
[tex]a^n \left(1 + a + a^2 + a^3 + a^4\right)[/tex]
but there's not much to say about divisibility here without any more information about a.
If you meant
[tex]a^n + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4)[/tex]
simplifying gives
[tex]5a^n + 10 = 5 (a^n+2)[/tex]
which is clearly divisible by 5.
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