Functie legata de ordin

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Vlad Matei
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Functie legata de ordin

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Fie \( a>1 \) un numar natural si definim \( ord_{p}(a)=0 \) pentru \( p|a \) si in rest in modul uzual. Definim functia \( f:\{2,3,5,...\}\rightarrow \mathbf{N^*} \) prin \( \displaystyle f(p)=\frac{p-1}{ord_{p}(a)} \). Demonstrati ca \( f \) este nemarginita.

Obs: Functia este definita pe multimea numerelor prime.

American Mathematical Monthly
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