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Contests
International Contests
IMO Longlists
1986 IMO Longlists
40
40
Part of
1986 IMO Longlists
Problems
(1)
Max. value of 2m+7n
Source:
8/29/2010
Find the maximum value that the quantity
2
m
+
7
n
2m+7n
2
m
+
7
n
can have such that there exist distinct positive integers
x
i
(
1
≤
i
≤
m
)
,
y
j
(
1
≤
j
≤
n
)
x_i \ (1 \leq i \leq m), y_j \ (1 \leq j \leq n)
x
i
(
1
≤
i
≤
m
)
,
y
j
(
1
≤
j
≤
n
)
such that the
x
i
x_i
x
i
's are even, the
y
j
y_j
y
j
's are odd, and
∑
i
=
1
m
x
i
+
∑
j
=
1
n
y
j
=
1986.
\sum_{i=1}^{m} x_i +\sum_{j=1}^{n} y_j=1986.
∑
i
=
1
m
x
i
+
∑
j
=
1
n
y
j
=
1986.
function
algebra unsolved
algebra