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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2003 All-Russian Olympiad Regional Round
8.8
8.8
Part of
2003 All-Russian Olympiad Regional Round
Problems
(1)
a,b, a+b, a-b incudes in 2003 pos. int. - All-Russian MO 2003 Regional (R4) 8.8
Source:
9/17/2024
A set of
2003
2003
2003
positive numbers is such that for any two numbers
a
a
a
and
b
b
b
included in it (
a
>
b
a > b
a
>
b
) at least one of the numbers
a
+
b
a + b
a
+
b
or
a
ā
b
a - b
a
ā
b
also included in the set. Prove that if these numbers are ordered by increasing, then the differences between adjacent numbers will be the same.
number theory