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Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
2016 Poland - Second Round
4
4
Part of
2016 Poland - Second Round
Problems
(1)
Show that exists positive integer
Source: 67 Polish MO 2016 Second Round - Problem 4
4/30/2018
Let
k
k
k
be a positive integer. Show that exists positive integer
n
n
n
, such that sets
A
=
{
1
2
,
2
2
,
3
3
,
.
.
.
}
A = \{ 1^2, 2^2, 3^3, ...\}
A
=
{
1
2
,
2
2
,
3
3
,
...
}
and
B
=
{
1
2
+
n
,
2
2
+
n
,
3
2
+
n
,
.
.
.
}
B = \{1^2 + n, 2^2 + n, 3^2 + n, ... \}
B
=
{
1
2
+
n
,
2
2
+
n
,
3
2
+
n
,
...
}
have exactly
k
k
k
common elements.
number theory
set
Perfect Squares
Poland