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Israel Olympic Revenge
2018 Israel Olympic Revenge
1
1
Part of
2018 Israel Olympic Revenge
Problems
(1)
Primes divide sequence
Source: Israel 2018 Olympic Revenge
3/22/2020
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
)
prime numbers
Divisibility
number theory
Divisors