ISSN 1991-3087

:   77-24978 05.07.2006 .

ISSN 1991-3087

42457

- 1 .

: 305008, ., , .7.

.: 8-910-740-44-28

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Ax+By=Cz (1)

A,B,C,x,y.z - , x,y,z > 2, A,B,C .

A,B,C :

A=ta, B=ub, C=vc,

a,b,c - ,

Ax= (ta)x=txax, By= (ub)y=uyby, Cz= (vc)z=vzcz

(1)

txax+uyby=vz cz (2)

(2) ta, ub,vc, , a,b,c, . , , .

33+63=35

A=1*3, t=1, a=3

B=2*3,u=2,b=3

C=1*3,v=1,c=3

,

A3+B3=C5

33+63=35,

1333+2333=1535

a3+8b3=c5

() (txax+uyby ) (a3+b3).

(txax+uyby)=q(a3+b3)+r, q ,r , 0≤ r<(a3+b3), q#0

q=1, r=0, A=a, B=b, x=3, y=3,

, , x,y>2.

(2) :

q(a3+b3)+r = vz cz

q(a3+b3)= vz cz -r (3)

(3) , ,

q(a3+b3)=qp(a+b) (4)

q#0, (4)

(a3+b3)=p(a+b) (5)

p=a2-ab+b2

(5) a=b

2a3=a22a (6)

, a=b (5).

, (5) .

c

(a+b)3-3ab(a+b)-p(a+b )=0 (7)

, :

(a+b)((a+b)2-3ab-p)=0 (8)

,

a+b=0 (9)

(a+b)2-3ab-p=0 (10)

(9) a= -b, .

(10) :

1)                 a2-ab=p-b2 (11)

2)                 b2-ab=p-a2 (12)

(12) (11)

a b , a#b , .. , , , , a b .

(12) (5), , : a=b, a Ax(A) By(B) . , Cz (C) , a=b=c.

: .

 

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An+Bn=Cn (1)

A,B,C n>2.

, (1) .

a,b,c, a,b,c- A,B,C, .

, , a=b=c, .

, , A,B,C , .

, , (1) n>2.

 

 

1.                  .. . ,8., ., - ,1999.

2.                  http://www.ams.org//profession/prizes-awards/ams-supported/beal-prize.

 

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