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Czech and Slovak Olympiad III A
2006 Czech and Slovak Olympiad III A
5
triples of 3 primes
triples of 3 primes
Source: Czech and Slovak third round,2006,p5
March 3, 2012
number theory proposed
number theory
Problem Statement
Find all triples
(
p
,
q
,
r
)
(p,q,r)
(
p
,
q
,
r
)
of pairwise distinct primes such that
p
∣
q
+
r
,
q
∣
r
+
2
p
,
r
∣
p
+
3
q
.
p\mid q+r, q\mid r+2p, r\mid p+3q.
p
∣
q
+
r
,
q
∣
r
+
2
p
,
r
∣
p
+
3
q
.
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