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13. príklad 1. zimnej série 2008/2009

Zadanie:
Postupnosť $\{a_i\}_{i=1}^\infty$ je definovaná nasledovne:

$a_1=1,$

$a_2=2,$

$a_3=24,$

$a_n=\frac{6a_{n-1}^2a_{n-3}-8a_{n-1}a_{n-2}^2}{a_{n-2}a_{n-3}}, n>3.$

Dokážte, že $n$ delí $a_n$ pre každé prirodzené číslo $n$ .

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