Whakaoti i te P=NP

$$P = N P$$

Whakaoti mō N (complex solution)

$$\left\{\begin{matrix}\\N=1\text{, }&\text{unconditionally}\\N\in \mathrm{C}\text{, }&P=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$NP=P$$

He hanga arowhānui tō te whārite.

$$PN=P$$

Whakawehea ngā taha e rua ki te P.

$$\frac{PN}{P}=\frac{P}{P}$$

Mā te whakawehe ki te P ka wetekia te whakareanga ki te P.

$$N=\frac{P}{P}$$

Whakawehe P ki te P.

$$N=1$$

Whakaoti mō P (complex solution)

$$\left\{\begin{matrix}\\P=0\text{, }&\text{unconditionally}\\P\in \mathrm{C}\text{, }&N=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te NP mai i ngā taha e rua.

$$P-NP=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te P.

$$\left(1-N\right)P=0$$

Whakawehe 0 ki te 1-N.

$$P=0$$

Whakaoti mō N

$$\left\{\begin{matrix}\\N=1\text{, }&\text{unconditionally}\\N\in \mathrm{R}\text{, }&P=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$NP=P$$

He hanga arowhānui tō te whārite.

$$PN=P$$

Whakawehea ngā taha e rua ki te P.

$$\frac{PN}{P}=\frac{P}{P}$$

Mā te whakawehe ki te P ka wetekia te whakareanga ki te P.

$$N=\frac{P}{P}$$

Whakawehe P ki te P.

$$N=1$$

Whakaoti mō P

$$\left\{\begin{matrix}\\P=0\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&N=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te NP mai i ngā taha e rua.

$$P-NP=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te P.

$$\left(1-N\right)P=0$$

Whakawehe 0 ki te 1-N.

$$P=0$$