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2011 CentroAmerican
4
4
Part of
2011 CentroAmerican
Problems
(1)
Diophantine equation with primes
Source: Centroamerican 2011, Problem 4
6/22/2011
Find all positive integers
p
p
p
,
q
q
q
,
r
r
r
such that
p
p
p
and
q
q
q
are prime numbers and
1
p
+
1
+
1
q
+
1
−
1
(
p
+
1
)
(
q
+
1
)
=
1
r
.
\frac{1}{p+1}+\frac{1}{q+1}-\frac{1}{(p+1)(q+1)} = \frac{1}{r}.
p
+
1
1
+
q
+
1
1
−
(
p
+
1
)
(
q
+
1
)
1
=
r
1
.
number theory
prime numbers
number theory proposed