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Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2005 Bosnia and Herzegovina Junior BMO TST
2
2
Part of
2005 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
2 + 2\sqrt{1 + 28n^2} is an integer, then it is the square of an integer
Source: 2005 Bosnia & Herzegovina JBMO TST p2
5/27/2020
Let n be a positive integer. Prove the following statement: ”If
2
+
2
1
+
28
n
2
2 + 2\sqrt{1 + 28n^2}
2
+
2
1
+
28
n
2
is an integer, then it is the square of an integer.”
Perfect Square
Integer
number theory