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Miklós Schweitzer
1985 Miklós Schweitzer
7
7
Part of
1985 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1985, Problem 7
Source: Miklós Schweitzer 1985
9/5/2016
Let
p
1
p_1
p
1
and
p
2
p_2
p
2
be positive real numbers. Prove that there exist functions
f
i
:
R
→
R
f_i\colon \mathbb R \rightarrow \mathbb R
f
i
:
R
→
R
such that the smallest positive period of
f
i
f_i
f
i
is
p
i
(
i
=
1
,
2
)
p_i\, (i=1, 2)
p
i
(
i
=
1
,
2
)
, and
f
1
−
f
2
f_1-f_2
f
1
−
f
2
is also periodic. [J. Riman]
Miklos Schweitzer
college contests
function
real analysis