629.4

. . ()

.

.

.

The proof of algebraic solution of the Great theorem of Ferm has been presented.

-

n n nx y z+ = (1) 3n - - . , , , .

, , , - , -- , . - - , , .

, , 0b a> > , Y X a= + , Z X b= + -

( ) ( )11

nn i i i i n n

ni

X C b a X b a

= + . (2)

, - . - . (1)

( )11

nn i i i i

ni

X C b a X kX

= + , (3)

( )n nkX b a= . -

, k 0b a> > , 3n , . . (2). (3) (2) -

1n - n , ( )1n - .

, n ( )1n -, , - :

1 1 1n n

n n n nbk ak

b a b a + + = . (4)

2n > b , a , k n - 3n = . n - X , . -, (4) -, .

, a a= a a . - (4), ,

( ) 1nn n nk b a = ( )( )1 1

1

n n ii i i i n nnk b a b a

, (5) , , k

( )n nb a

mk

= ,

, ( )n nb a k m = . -

( )( )( )1

1 2

n

n nn n

mkb a

=

( )( ) ( ) ( )22 21 1 1Cn i n i n ni n i i i n n n nni

m b a b a n b a + ,

61

( ) 1nn nb a

mk

= . m

111n

mk

=

( )( )12 21 n in ni i i n nni

C b a b ak

( )( ) ( )11 1 nn n n nn b a b a . (6) (6) , m

k , a , b 3n . -, (1) , , - - (4), -, .

(6) , - - m 1nk .

, (6) - 2, 2n = , [ ]( )0 2

1, , ,i f k n a b , -

0. , - 1, 5, 12, 13

7a = 8b = 3k = , 15m = . (6) a , b 2 2 15b a = ,

, 3k = , 5m = . - m , (6) - - . (6) 1nk , (6) - m :

( )( )2 211

1n nn i i i i n n

nm k C k b a b a =

( )( ) ( 1)1 1 1 nn n n n nk n b a b a , (7)

1 d+ , m 1d =

( ) ( )( )1 1 1

2_

n n nnn n

n n

k b a nb a

b a

+

( ) ( )2

1

1 n i i i inn n

C k b ab a

= ,

. . k 2n > .

(6) . 2b = 1a = 3n = ; 1b a = 2 2 3b a =

2 2 7b a = . (2)

3 23 9 7x x x= + + . 5,0455x , : 1,38489k ; 35,382m (6) ( )1 0,521398 0,309462 0,183673m = =

35,382= , k r= , 6,8m .

, , 5n = , 3b = , 1a = , - -

(7) .

( )45 5 4242b a = .

16,0803466x = , 15,049427k = ,

4 8242 15,049427 2,279 10m = .

1. . . . .

.: , 1970. 2. . . . .:

, 1961. 3. . . . .: ,

1965. 4. . .

. .: , 1992. 5. . .

. .: , 1984.

16.01.07.

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