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National and Regional Contests
Hungary Contests
Kürschák Math Competition
1966 Kurschak Competition
1966 Kurschak Competition
Part of
Kürschák Math Competition
Subcontests
(3)
3
1
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two infinite sets of non-negative integers
Do there exist two infinite sets of non-negative integers such that every non-negative integer can be uniquely represented in the form
a
+
b
a + b
a
+
b
with
a
a
a
in
A
A
A
and
b
b
b
in
B
B
B
?
2
1
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(5 +\sqrt{26})^n has equal n digits after the decimal point
Show that the
n
n
n
digits after the decimal point in
(
5
+
26
)
n
(5 +\sqrt{26})^n
(
5
+
26
)
n
are all equal.
1
1
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5 points in space to form a pentagon
Can we arrange
5
5
5
points in space to form a pentagon with equal sides such that the angle between each pair of adjacent edges is
9
0
o
90^o
9
0
o
?