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2010 IFYM, Sozopol
5
Perfect square
Perfect square
Source:
July 4, 2011
number theory
greatest common divisor
Diophantine equation
number theory unsolved
Problem Statement
Let n is a natural number,for which
1
+
12
n
2
\sqrt{1+12n^2}
1
+
12
n
2
is a whole number.Prove that
2
+
2
1
+
12
n
2
2+2\sqrt{1+12n^2}
2
+
2
1
+
12
n
2
is perfect square.
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