MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey EGMO TST
2017 Turkey EGMO TST
6
Turkey EGMO TST 2017 P6
Turkey EGMO TST 2017 P6
Source: Turkey EGMO TST 2017 P6
June 1, 2017
Turkey
EGMO
TST
number theory
contest problem
order of an element
Problem Statement
Find all pairs of prime numbers
(
p
,
q
)
(p,q)
(
p
,
q
)
, such that
(
2
p
2
−
1
)
q
+
1
p
+
q
\frac{(2p^2-1)^q+1}{p+q}
p
+
q
(
2
p
2
−
1
)
q
+
1
and
(
2
q
2
−
1
)
p
+
1
p
+
q
\frac{(2q^2-1)^p+1}{p+q}
p
+
q
(
2
q
2
−
1
)
p
+
1
are both integers.
Back to Problems
View on AoPS