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International Contests
IMO Longlists
1974 IMO Longlists
21
21
Part of
1974 IMO Longlists
Problems
(1)
Prove that M =ℤ+ [ILL 1974]
Source:
1/2/2011
Let
M
M
M
be a nonempty subset of
Z
+
\mathbb Z^+
Z
+
such that for every element
x
x
x
in
M
,
M,
M
,
the numbers
4
x
4x
4
x
and
⌊
x
⌋
\lfloor \sqrt x \rfloor
⌊
x
⌋
also belong to
M
.
M.
M
.
Prove that
M
=
Z
+
.
M = \mathbb Z^+.
M
=
Z
+
.
floor function
algebra proposed
algebra