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1983 All Soviet Union Mathematical Olympiad
367
367
Part of
1983 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 367 All Soviet Union MO 1983 2m+1 integers with abs.value <=2m-1
Source:
7/28/2019
Given
(
2
m
+
1
)
(2m+1)
(
2
m
+
1
)
different integers, each absolute value is not greater than
(
2
m
ā
1
)
(2m-1)
(
2
m
ā
1
)
. Prove that it is possible to choose three numbers among them, with their sum equal to zero.
combinatorics
number theory