Page 80 - Numbertheory

@ @Hßìÿa@ö§aI@†a‡Èÿa@óî‹Åä@@

:

(n + 3) | (n 2 + 7) (n + 3) | (n 2 + 3n )

. (n + 3) |16 . (n + 3) | (3n + 9) . (n + 3) | (3n − 7)
. n = 13 n = 5 n = 1

9 6a3 + 2b 5 [Aust.MC 1982] ( )

17 ( ) ba 9( ) 2 ()

11 ( )

6a3 + 2b5 = 600 +10a + 3 + 200 +10b + 5 :( )

= 9(89 + a + b ) + (a + b + 7)

a+b +7 . 0 ≤ a +b ≤18 0 ≤ b ≤ 9 0 ≤ a ≤ 9

. a + b = 11 a +b = 2 9

. 11

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