MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
1996 Iran MO (3rd Round)
6
Find all pairs of primes
Find all pairs of primes
Source: Iran Third Round 1997, E3, P7
March 25, 2011
modular arithmetic
number theory proposed
number theory
Problem Statement
Find all pairs
(
p
,
q
)
(p,q)
(
p
,
q
)
of prime numbers such that
m
3
p
q
≡
m
(
m
o
d
3
p
q
)
∀
m
∈
Z
.
m^{3pq} \equiv m \pmod{3pq} \qquad \forall m \in \mathbb Z.
m
3
pq
≡
m
(
mod
3
pq
)
∀
m
∈
Z
.
Back to Problems
View on AoPS