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Ireland National Math Olympiad
2004 Irish Math Olympiad
1
Primes and again primes
Primes and again primes
Source: Ireland 2004
January 2, 2007
number theory
prime numbers
Problem Statement
Determine all pairs of prime numbers
(
p
,
q
)
(p, q)
(
p
,
q
)
, with
2
≤
p
,
q
<
100
2 \leq p, q < 100
2
≤
p
,
q
<
100
, such that
p
+
6
,
p
+
10
,
q
+
4
,
q
+
10
p+6, p+10, q+4, q+10
p
+
6
,
p
+
10
,
q
+
4
,
q
+
10
and
p
+
q
+
1
p+q+1
p
+
q
+
1
are all prime numbers.
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