Page 126 - Numbertheory

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n 27 ( ) an [MAӨ 2011] ( )

29 ( ) a1 + a2 + ... + a10

25 ( ) 23 ( )

:( )
. a1 + a2 + ... + a10 = 1+ 2 + 2 + 3 + 2 + 4 + 2 + 4 + 3 + 4 = 27

mn = 40 nm ()

13 ( ) m +n 2m + 3n = 31

12 ( ) 8( ) 5()

. n = 40 mn = 40 :( )

m

2m +  40  = 31
3 m 

2m 2 − 31m +120 = 0

(2m −15) (m − 8) = 0

.m =8 m . m = 15 m =8

2 .n =5

. m + n = 8 + 5 =13

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