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2019 Junior Balkan MO
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2019 Junior Balkan MO, Problem 1
Source: 2019 Junior Balkan MO
6/22/2019
Find all prime numbers
p
p
p
for which there exist positive integers
x
x
x
,
y
y
y
, and
z
z
z
such that the number
x
p
+
y
p
+
z
p
−
x
−
y
−
z
x^p + y^p + z^p - x - y - z
x
p
+
y
p
+
z
p
−
x
−
y
−
z
is a product of exactly three distinct prime numbers.
number theory
Junior
JBMO
Balkan
2019
prime numbers