6,,3,4,, 3 4 8 6 6................................. 6..................................
, 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p, p 3,..., p n p, p,..., p n N, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 3, 9, 83, 89, 9, 0, 03, 0, 09, 3,, 3, 3, 39, 49,,, 63, 6, 3, 9, 8, 9, 93, 9, 99,, 3,, 9, 33, 39, 4,,, 63, 69,,, 8, 83, 93, 6 30, 3, 33, 3, 33, 33, 34, 349, 33, 39, 36, 33, 39, 383, 389, 39, 6 40, 409, 49, 4, 43, 433, 439, 443, 449, 4, 46, 463, 46, 49, 48, 49, 499, 03, 09,, 3, 4, 4,, 63, 69,,, 8, 93, 99, 4 60, 60, 63, 6, 69, 63, 64, 643, 64, 63, 69, 66, 63, 6, 683, 69, 6 0, 09, 9,, 33, 39, 43,,, 6, 69, 3, 8, 9, 4 809, 8, 8, 83, 8, 89, 839, 83, 8, 89, 863, 8, 88, 883, 88, 90, 9, 99, 99, 93, 94, 94, 93, 96, 9, 9, 983, 99, 99, 4 009, 03, 09, 0, 03, 033, 039, 049, 0, 06, 063, 069, 08, 09, 093, 09, 6 03, 09,, 3, 9,, 3, 63,, 8, 8, 93, 0, 3,, 3, 9, 3, 3, 49, 9,, 9, 83, 89, 9, 9, 30, 303, 30, 39, 3, 3, 36, 36, 33, 38, 399, 409, 43, 4, 49, 433, 439, 44, 4, 43, 49, 4, 48, 483, 48, 489, 493, 499,
, 3, 3, 43, 49, 3, 9, 6,, 9, 83, 9, 60, 60, 609, 63, 69, 6, 6, 63, 6, 663, 66, 669, 693, 69, 699, 4 09,, 3, 33, 4, 4, 3, 9,, 83, 8, 89, 80, 8, 83, 83, 84, 86, 86, 8, 83, 8, 89, 889, 90, 90, 93, 93, 933, 949, 9, 93, 99, 98, 993, 99, 999, 3 000 00 3, 36 48, 483, 48, 489 πx = x 0, 3,, π0 = 4, π = π00 00 π00 = π00 = + = 46,..., π000 = + + 4 = 68 πx x πx lim x x log x = log x e =.88... gx = x log x x = 0 n g0 n = 0n 0n = log e 0n n log e 0 = 0n n log 0 e e. = 3 3 /0 log 0 3 0.4 g0 n 0n n log 3 3 0 0 0n n 3 log 0 3 0n n 0.43 = 0 8 π0 8 g0 8 g0 8 0 8 0.43 40 8 π0 8 = 64 6% 00 = 0 0 n = 0 g0 0 0 0.43 =4 3 π0 0 = 40 3
4.8% 00 00 lix = x log t dt gx lix lix πx li0 8 609 π0 8 = 64 0.03% li0 0 406 π0 8 = 40 0.000% x πx lix gx 0 4 6. 4.3 0 30 0 3 68 8 3 0 4 9 46 086 0 99 9630 8686 0 6 8498 868 38 0 6649 66498 604 0 8 64 609 4868 0 9 08434 08493 48494 0 0 40 406 4349448 0 480483 4806640 4899 πx gx = x/ log x hx = x dt/ log t 896 ζs = n= n s = + s + 3 s + + n s + Riemann 3 ζs = p: = p s s 3 s s s + + s + s + + 3s 3 + s 3 + s + + s + s + 3s 3 + 3s + s + s + + + s + s + 3s + 3s 4
n n s ζs + p s + p s + p 3s + = p s lix πx 00! πx lix ± x ε πx lix lim = 0 x x +ε ζs s s / 0 00 A, 3,, 9, 3, 4, 3, 6, 3, 89, 9 B 3,,, 9, 3, 3, 43, 4, 9, 6,, 9, 83 p p = +, 3 = 4 + = +, 3 = 9 + 4 = 3 + 3,, 3 = +, = +, = + A 4 B 4 3 4 p p = x + y x, y p 4
4 3 p x +y p = x +y x, y, x = m +, y = n x + y = 4m + 4m + + 4n = 4m + m + n + 4 3 4 x + y = + p = x + y x, y p 09 = +, x + y = x + yix yi p = x + y = + i i, 3 = 3 + i3 i, = 4 + i4 i, 9 = + i i,... 09 = + i i,...!! 4 p = x + xy + y 3 p p = x + xy + y x, y p 3 3 ω x + xy + y = x + yωx + yω i 4 ω 3 4 3 6 p p = x + y x, y p 8 p = x + y x, y p 8 3 3 p = x y x, y p 8 4 6,,3 6
3 3 + + 9 + = π 4 0 0 dx + x = dx x = tan θ + x π/4 0 dtan θ π/4 + tan θ = dθ 0 + tan θ cos θ = π/4 0 dθ = π 4 x + x 4 x 6 + x 8 x 0 + 0 x < = x +x 0 dx + x = x + x 4 x 6 + x 8 x 0 + dx 0 ] = [x x3 3 + x x + x9 9 x + = 3 + + 9 + p: χp p = 3 + 0 + 3 + χp p 4 3, 3 + 3 3 + + + + + + + 3 3 3 + 3 + + 3 + 3 + 3 3 + 8 3 + + 3 + = π 4 Ls, χ = p: χp p s L, χ Ls, χ L
p 4 3 p = + p = x + xy + y 9 + + 3 = π 3 3 ± p p 3,, 4 0 sin π + sin 4π + sin 8π = sin 6π + sin 0π π + sin = sin π, sin 4π 3 / cos θ + i sin θ n = cos nθ + i sin nθ n n 0 a = cos π + i sin π a = cos 4π + i sin 4π, a3 = cos 6π + i sin 6π, a4 = cos 8π + i sin 8π, a = cos 0π 0π + i sin, a6 = cos π π + i sin, a = cos π + i sin π = A = a + a + a 4, B = a 3 + a + a 6 A = cos π + cos 4π + cos 8π + i sin π + sin 4π + sin 8π 8
A, B A+B, AB a = 0 a a 6 + a + a 4 + a 3 + a + a + = 0 a = a 6 + a + a 4 + a 3 + a + a + = 0 A + B = a + a + a 3 + a 4 + a + a 6 =, AB = a + a + a 4 a 3 + a + a 6 = a 4 + a + a 3 + a + a 3 = a 4 + a + a + 3a 3 + a 4 + a + a 6 = a 4 + a + a + a 3 + a 4 + a + a 6 + a 3 = a 4 a 3 = a = A, B t + t + = 0 A, B = ± i sin π, sin 4π > 0, sin 8π < 0 sin 4π + sin 8π > 0 ImA = sin π + sin 4π + sin 8π > 0 + 0 = 0 A = + i, B = i {a, a, a 3, a 4, a, a 6 } {a, a, a 4 } {a 3, a, a 6 } {,, 3, 4,, 6} = {,, 4} {3,, 6} A = a + a + a 3, B = a 4 + a + a 6 3 A + B = A B a sin π 6π 8π 0π 8π + sin + sin + sin + sin = {,, 3,..., 0} = {, 3, 4,, 9} {, 6,, 8, 0} 3 cos π 6π 8π + cos + cos 3 3 3 cos 4π 0π π + cos + cos 3 3 3 sin π 6π 8π + sin + sin 3 3 3 = sin 4π 0π π + sin + sin 3 3 3 = 8π 0π 4π = cos + cos + cos 3 3 4π 6π π = cos + cos + cos 3 3 sin 8π 3 + sin 0π 3 + sin 4π 3 sin 4π 6π π + sin + sin 3 3 3 3 = + 3 4 3 = 3 4 = = 3 3 3 3 + 3 3 9
96 cos π = + + + + 3 + 6 8 4 4 63 cos π = +, sin π 4 = + 000 0 0 p = χ p χ p = { p,, 4 p 3,, 6 0 {,, 3, 4,, 6} = {,, 4} {3,, 6} p p = x + xy + y x, y p,, 4 χ p = p: χ p p = + 3 + 3 = π p = χ p { p, 3, 4,, 9 χ p = p, 6,, 8, 0 0
3 p p = x + xy + 3y x, y χ p = p: χ p p = + 3 + 3 = π 0 π = 0. 8 8 8 0 99-006 3 6 6.
Fermat,, 008 :! vs! 6. 360, 0