MathDB
Problems
Contests
International Contests
Nordic
2017 Nordic
1
1
Part of
2017 Nordic
Problems
(1)
n^2+n+1-numbers
Source: Nordic Mathematical Contest 2017 Problem 1
4/4/2017
Let
n
n
n
be a positive integer. Show that there exist positive integers
a
a
a
and
b
b
b
such that
a
2
+
a
+
1
b
2
+
b
+
1
=
n
2
+
n
+
1.
\frac{a^2 + a + 1}{b^2 + b + 1} = n^2 + n + 1.
b
2
+
b
+
1
a
2
+
a
+
1
=
n
2
+
n
+
1.
algebra
number theory