10

Part of 2004 Romania Team Selection Test

Problems(1)

classical, but yet hard

Source: Romanian ROM TST 2004, problem 10, created by Calin Popescu

Prove that for all positive integers

n,m

m

odd, the following number is an integer

\frac 1{3^mn}\sum^m_{k=0} { 3m \choose 3k } (3n-1)^k.

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