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2017 USAJMO
4
4
Part of
2017 USAJMO
Problems
(1)
(a-2)(b-2)(c-2)+12 is prime and divides ...
Source: JMO 2017 P4
4/20/2017
Are there any triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of positive integers such that
(
a
−
2
)
(
b
−
2
)
(
c
−
2
)
+
12
(a-2)(b-2)(c-2)+12
(
a
−
2
)
(
b
−
2
)
(
c
−
2
)
+
12
is a prime number that properly divides the positive number
a
2
+
b
2
+
c
2
+
a
b
c
−
2017
a^2+b^2+c^2+abc-2017
a
2
+
b
2
+
c
2
+
ab
c
−
2017
?
JMO
2017 USAJMO
USAJMO