Dana je binarna operacija
![*](/media/m/7/b/1/7b1c542584d6310e587a344b5199765f.png)
nad prirodnim brojevima takva da vrijedi:
i)
![1 * n = n + 1 \quad \forall n \in \mathbb{N}](/media/m/b/b/4/bb4923ad2eef3cbe1c23ac0617741ac2.png)
,
ii)
![m * 1 = (m - 1) * 2 \quad \forall m > 1](/media/m/9/f/b/9fbf93427396a850a2002f7a2b701e95.png)
,
iii)
![m * n = (m - 1) * (m * (n - 1)) \quad \forall m, n > 1](/media/m/2/3/1/231e039e8f73fbf622d9a2c790cae1d3.png)
.
Nađite
![3*3](/media/m/c/f/9/cf9aee52276c237e71e1afd1d728896f.png)
.
%V0
Dana je binarna operacija $*$ nad prirodnim brojevima takva da vrijedi:
i) $1 * n = n + 1 \quad \forall n \in \mathbb{N}$,
ii) $m * 1 = (m - 1) * 2 \quad \forall m > 1$,
iii) $m * n = (m - 1) * (m * (n - 1)) \quad \forall m, n > 1$.
Nađite $3*3$.