Whakaoti i te (+mathfrak{F}(2+1)(2^{2}+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

$$( + \mathfrak { F } ( 2 + 1 ) ( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 ) ( 2 ^ { 32 } + 1 ) + 1$$

Aromātai

$$18446744073709551615F+1$$

Ngā Upane Otinga

Tāpirihia te 2 ki te 1, ka 3.

$$F\times 3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$F\times 3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tāpirihia te 4 ki te 1, ka 5.

$$F\times 3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Whakareatia te 3 ki te 5, ka 15.

$$F\times 15\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tātaihia te 2 mā te pū o 4, kia riro ko 16.

$$F\times 15\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tāpirihia te 16 ki te 1, ka 17.

$$F\times 15\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Whakareatia te 15 ki te 17, ka 255.

$$F\times 255\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tātaihia te 2 mā te pū o 8, kia riro ko 256.

$$F\times 255\left(256+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tāpirihia te 256 ki te 1, ka 257.

$$F\times 255\times 257\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Whakareatia te 255 ki te 257, ka 65535.

$$F\times 65535\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

Tātaihia te 2 mā te pū o 16, kia riro ko 65536.

$$F\times 65535\left(65536+1\right)\left(2^{32}+1\right)+1$$

Tāpirihia te 65536 ki te 1, ka 65537.

$$F\times 65535\times 65537\left(2^{32}+1\right)+1$$

Whakareatia te 65535 ki te 65537, ka 4294967295.

$$F\times 4294967295\left(2^{32}+1\right)+1$$

Tātaihia te 2 mā te pū o 32, kia riro ko 4294967296.

$$F\times 4294967295\left(4294967296+1\right)+1$$

Tāpirihia te 4294967296 ki te 1, ka 4294967297.

$$F\times 4294967295\times 4294967297+1$$

Whakareatia te 4294967295 ki te 4294967297, ka 18446744073709551615.

$$F\times 18446744073709551615+1$$

Kimi Pārōnaki e ai ki F

$$18446744073709551615$$

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Tapeke

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 15\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tātaihia te 2 mā te pū o 4, kia riro ko 16.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 15\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tāpirihia te 16 ki te 1, ka 17.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 15\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Whakareatia te 15 ki te 17, ka 255.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 255\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tātaihia te 2 mā te pū o 8, kia riro ko 256.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 255\left(256+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tāpirihia te 256 ki te 1, ka 257.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 255\times 257\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Whakareatia te 255 ki te 257, ka 65535.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 65535\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

Tātaihia te 2 mā te pū o 16, kia riro ko 65536.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 65535\left(65536+1\right)\left(2^{32}+1\right)+1)$$

Tāpirihia te 65536 ki te 1, ka 65537.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 65535\times 65537\left(2^{32}+1\right)+1)$$

Whakareatia te 65535 ki te 65537, ka 4294967295.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 4294967295\left(2^{32}+1\right)+1)$$

Tātaihia te 2 mā te pū o 32, kia riro ko 4294967296.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 4294967295\left(4294967296+1\right)+1)$$

Tāpirihia te 4294967296 ki te 1, ka 4294967297.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 4294967295\times 4294967297+1)$$

Whakareatia te 4294967295 ki te 4294967297, ka 18446744073709551615.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 18446744073709551615+1)$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$18446744073709551615F^{1-1}$$

Tango 1 mai i 1.

$$18446744073709551615F^{0}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$18446744073709551615\times 1$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$18446744073709551615$$