Page 128 - Numbertheory

@ @@Hßìÿaö§aI@†a‡Èÿa@óî‹Åä@

N = pq 2 . pk 648 = 23 × 34
. 23 × 34 1, p , q , q 2, pq , pq 2
. p 3q 6
. 32 = 9
q =3 p =2

x 2002 = x × y × z ×w [British SMC 2002] ( )

x 2 + y 2 + z 2 +w 2 wzy

343 ( ) 285 ( ) 203 ( ) 66 ( )

. 2002 = 2× 7 ×11×13 :( )

x 2 + y 2 + z 2 +w 2 = 22 + 72 +112 +132 = 343

. [British SMC 1999] ( )

55552 + 66662 ( ) 10002 +1112 ( )
10012 +10022 ( ) 20002 − 9992 ( )

30858025 + 44435556 = 75293581 ( ) :( )

0 (1+ 5 + 9 + 5) − (8 + 3 + 2 + 7) = 0

( ) . 11 () 11

20002 − 9992 = (2000 − 999) (2000 + 999)= (1001) × 2999

.1+ 4 = 5 () .

.() .5

١١٥