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Spain Mathematical Olympiad
2018 Spain Mathematical Olympiad
1
1
Part of
2018 Spain Mathematical Olympiad
Problems
(1)
2x+1 is a perfect square but the following x+1 integers are not.
Source: Spain Mathematical Olympiad 2018 P1
3/17/2018
Find all positive integers
x
x
x
such that
2
x
+
1
2x+1
2
x
+
1
is a perfect square but none of the integers
2
x
+
2
,
2
x
+
3
,
…
,
3
x
+
2
2x+2, 2x+3, \ldots, 3x+2
2
x
+
2
,
2
x
+
3
,
…
,
3
x
+
2
are perfect squares.
algebra
Spain
number theory