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Found problems: 2

2004 Nicolae Păun, 1
Tags: decomposition , injectivity , algebra , function
Prove that any function that maps the integers to themselves is a sum of any finite number of injective functions that map the integers to themselves. [i]Sorin Rădulescu[/i] and [i]Ion Savu[/i]

2009 Bosnia And Herzegovina - Regional Olympiad, 3
Tags: decomposition , combinatorics
Decomposition of number $n$ is showing $n$ as a sum of positive integers (not neccessarily distinct). Order of addends is important. For every positive integer $n$ show that number of decompositions is $2^{n-1}$