such that 
is unbounded and![\[2f(m)f(n)-f(n-m)-1\]](http://latex.artofproblemsolving.com/0/f/7/0f77b5addbf8f5e603eb1b6923cdac795cd132e9.png)
is a perfect square for all integer 
Y by PikaPika999
Consider the set 
of all sequences of integers 
such that 
and let 
. Show that
![\[\sum_{s\in A} M(s)=(n+1)^{k+1}-(1^k+2^k+\ldots +(n+1)^k).\]](//latex.artofproblemsolving.com/7/6/e/76e7fce0da6bb9537b73d8699f7a21a6b8cb61fa.png)
Ioan Tomescu
of all sequences of integers 
such that 
and let 
. Show that![\[\sum_{s\in A} M(s)=(n+1)^{k+1}-(1^k+2^k+\ldots +(n+1)^k).\]](http://latex.artofproblemsolving.com/7/6/e/76e7fce0da6bb9537b73d8699f7a21a6b8cb61fa.png)
Ioan Tomescu
Sum of max of some sequences is sum of powers
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Source: Romanian IMO TST 1981, Day 3 P1
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