Difference between revisions of "2002 Indonesia MO Problems/Problem 1"
(Solution to Problem 1)
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[[Category:Number Theory Problems]]
Revision as of 13:10, 14 July 2018
Show that is divisible by for any integers .
In order for to be divisible by , it must be divisible by and . Note that can be factored into .
If is even, then . If , then , and if , then . That means for all positive , is divisible by .
If , then . If , then . If , then . That means for all positive , is divisible by .
Because is divisible by and , it must be divisible by .