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PEN A Problems
112
A 112
A 112
Source:
May 25, 2007
algebra
Vieta
induction
number theory
relatively prime
Divisibility Theory
pen
Problem Statement
Prove that there exist infinitely many pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of relatively prime positive integers such that
a
2
−
5
b
and
b
2
−
5
a
\frac{a^{2}-5}{b}\;\; \text{and}\;\; \frac{b^{2}-5}{a}
b
a
2
−
5
and
a
b
2
−
5
are both positive integers.
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