MathDB
Problems
Contests
National and Regional Contests
Israel Contests
Israel Olympic Revenge
2018 Israel Olympic Revenge
1
Primes divide sequence
Primes divide sequence
Source: Israel 2018 Olympic Revenge
March 22, 2020
prime numbers
Divisibility
number theory
Divisors
Problem Statement
Let
n
n
n
be a positive integer. Prove that every prime
p
>
2
p > 2
p
>
2
that divides
(
2
−
3
)
n
+
(
2
+
3
)
n
(2-\sqrt{3})^n + (2+\sqrt{3})^n
(
2
−
3
)
n
+
(
2
+
3
)
n
satisfy
p
=
1
(
m
o
d
3
)
p=1 (mod3)
p
=
1
(
m
o
d
3
)
Back to Problems
View on AoPS