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2019 JBMO Shortlist
N2
JBMO Shortlist 2019 N2
JBMO Shortlist 2019 N2
Source:
September 12, 2020
number theory
Problem Statement
Find all triples
(
p
,
q
,
r
)
(p, q, r)
(
p
,
q
,
r
)
of prime numbers such that all of the following numbers are integers
p
2
+
2
q
q
+
r
,
q
2
+
9
r
r
+
p
,
r
2
+
3
p
p
+
q
\frac{p^2 + 2q}{q+r}, \frac{q^2+9r}{r+p}, \frac{r^2+3p}{p+q}
q
+
r
p
2
+
2
q
,
r
+
p
q
2
+
9
r
,
p
+
q
r
2
+
3
p
Proposed by Tajikistan
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