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National and Regional Contests
Poland Contests
Poland - Second Round
1965 Poland - Second Round
1965 Poland - Second Round
Part of
Poland - Second Round
Subcontests
(3)
6
1
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there is no polyhedron whose every plane section is a triangle.
Prove that there is no polyhedron whose every plane section is a triangle.
5
1
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square cannot be divided into 5 squares.
Prove that a square can be divided into any number greater than 5 squares, but cannot be divided into 5 squares.
4
1
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4p^2 + 1 and 6p^2 + 1 are also primes
Find all prime numbers
p
p
p
such that
4
p
2
+
1
4p^2 + 1
4
p
2
+
1
and
6
p
2
+
1
6p^2 + 1
6
p
2
+
1
are also prime numbers.