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3
3
Part of
PEN A Problems
Problems
(1)
A 3
Source:
5/25/2007
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.
algebra
polynomial
Vieta
function
induction
Divisibility Theory
pen