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\sqrt{n + 3}+ \sqrt{n +\sqrt{n + 3}} is integer (2016 Romanian NMO grade VII P1)
\sqrt{n + 3}+ \sqrt{n +\sqrt{n + 3}} is integer (2016 Romanian NMO grade VII P1)
Source:
September 3, 2024
number theory
Integer
Problem Statement
Find all non-negative integers
n
n
n
so that
n
+
3
+
n
+
n
+
3
\sqrt{n + 3}+ \sqrt{n +\sqrt{n + 3}}
n
+
3
+
n
+
n
+
3
is an integer.
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