MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
3
A 3
A 3
Source:
May 25, 2007
algebra
polynomial
Vieta
function
induction
Divisibility Theory
pen
Problem Statement
Let
a
a
a
and
b
b
b
be positive integers such that
a
b
+
1
ab+1
ab
+
1
divides
a
2
+
b
2
a^{2}+b^{2}
a
2
+
b
2
. Show that
a
2
+
b
2
a
b
+
1
\frac{a^{2}+b^{2}}{ab+1}
ab
+
1
a
2
+
b
2
is the square of an integer.
Back to Problems
View on AoPS