2002 Indonesia MO Problems/Problem 1
Show that is divisible o by for any integers .
In order for to be divisible by , must be divisible by and .
Lemma 1: is divisible by 4
Note that can be factored into . If is even, then . If , then , and if , then . That means for all positive , is divisible by .
Lemma 2: is divisible by 3
Again, note that can be factored into . If , then . If , then . If , then . That means for all positive , is divisible by .
Because is divisible by and , must be divisible by .
|2002 Indonesia MO (Problems)|
|1 • 2 • 3 • 4 • 5 • 6 • 7||Followed by|
|All Indonesia MO Problems and Solutions|