Functie polinomiala asumand ca valori numai cuburi perfecte

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Filip Chindea
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Functie polinomiala asumand ca valori numai cuburi perfecte

Post by Filip Chindea »

Fie \( f \in \mathbb{Z}[X] \), \( \deg f = 3 \) astfel incat pentru orice \( n \in \mathbb{N} \) exista \( k_n \in \mathbb{N} \) cu \( f(n) = k_n^3 \).
Aratati ca exista \( a, b \in \mathbb{Z} \) astfel incat \( f = (aX + b)^3 \).

[ Kvant M1823 si Teste tip OIM 2008 - Problema 3/Test 6 ]
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