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Austrian-Polish
2006 Austrian-Polish Competition
7
7
Part of
2006 Austrian-Polish Competition
Problems
(1)
sum, floors
Source: APMC 2006, Problem 7
9/9/2006
Find all nonnegative integers
m
,
n
m,n
m
,
n
so that
∑
k
=
1
2
m
⌊
k
n
2
m
⌋
∈
{
28
,
29
,
30
}
\sum_{k=1}^{2^{m}}\lfloor \frac{kn}{2^{m}}\rfloor\in \{28,29,30\}
k
=
1
∑
2
m
⌊
2
m
kn
⌋
∈
{
28
,
29
,
30
}
floor function
algebra proposed
algebra