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1989 Brazil National Olympiad
2
2
Part of
1989 Brazil National Olympiad
Problems
(1)
k(k+1)/3 is square iff k is square
Source: 11th Brazilian Math Olympiad - Problem 2
12/27/2017
Let
k
k
k
a positive integer number such that
k
(
k
+
1
)
3
\frac{k(k+1)}{3}
3
k
(
k
+
1
)
is a perfect square. Show that
k
3
\frac{k}{3}
3
k
and
k
+
1
k+1
k
+
1
are both perfect squares.
Brazilian Math Olympiad 1989
Brazilian Math Olympiad
number theory
Perfect Squares
Pell equations