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Swedish Mathematical Competition
2019 Swedish Mathematical Competition
6
6
Part of
2019 Swedish Mathematical Competition
Problems
(1)
a_n + a_{n + 1} always a perfect square
Source: 2019 Swedish Mathematical Competition p6
5/1/2021
Is there an infinite sequence of positive integers
{
a
n
}
n
=
1
∞
\{a_n\}_{n = 1}^{\infty}
{
a
n
}
n
=
1
∞
which contains each positive integer exactly once and is such that the number
a
n
+
a
n
+
1
a_n + a_{n + 1}
a
n
+
a
n
+
1
is a perfect square for each
n
n
n
?
Sequence
Perfect Square
number theory