MathDB
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Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2020 Latvia Baltic Way TST
13
13
Part of
2020 Latvia Baltic Way TST
Problems
(1)
Modified well - known NT problem
Source: Latvian TST for Baltic Way 2020 P13
10/18/2020
It is given that
n
n
n
and
12
n
2
+
1
\sqrt{12n^2+1}
12
n
2
+
1
are both positive integers. Prove that:
12
n
2
+
1
+
1
2
\sqrt{ \frac{\sqrt{12n^2+1}+1}{2}}
2
12
n
2
+
1
+
1
is also positive integer.
number theory