MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
6
A 6
A 6
Source:
May 25, 2007
algebra
polynomial
Vieta
Divisibility Theory
pen
Problem Statement
[*] Find infinitely many pairs of integers
a
a
a
and
b
b
b
with
1
<
a
<
b
1<a<b
1
<
a
<
b
, so that
a
b
ab
ab
exactly divides
a
2
+
b
2
−
1
a^{2}+b^{2}-1
a
2
+
b
2
−
1
. [*] With
a
a
a
and
b
b
b
as above, what are the possible values of
a
2
+
b
2
−
1
a
b
?
\frac{a^{2}+b^{2}-1}{ab}?
ab
a
2
+
b
2
−
1
?
Back to Problems
View on AoPS