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Romanian Masters of Mathematics Collection
2016 Romanian Master of Mathematics Shortlist
C4
C4
Part of
2016 Romanian Master of Mathematics Shortlist
Problems
(1)
u+v=x+y (mod 2016) in 46-element integer set with distinct {u, v}, {x,y}
Source: RMM Shortlist 2016 C4
7/4/2019
Prove that a
46
46
46
-element set of integers contains two distinct doubletons
{
u
,
v
}
\{u, v\}
{
u
,
v
}
and
{
x
,
y
}
\{x,y\}
{
x
,
y
}
such that
u
+
v
≡
x
+
y
u + v \equiv x + y
u
+
v
≡
x
+
y
(mod
2016
2016
2016
).
combinatorics
number theory
sets of integers