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18
2018 preRMO p18, diopantine 4abc = (a+3)(b+3)(c+3), a+b+c =?
2018 preRMO p18, diopantine 4abc = (a+3)(b+3)(c+3), a+b+c =?
Source:
August 7, 2019
Diophantine equation
diophantine
number theory
Problem Statement
If
a
,
b
,
c
≥
4
a, b, c \ge 4
a
,
b
,
c
≥
4
are integers, not all equal, and
4
a
b
c
=
(
a
+
3
)
(
b
+
3
)
(
c
+
3
)
4abc = (a+3)(b+3)(c+3)
4
ab
c
=
(
a
+
3
)
(
b
+
3
)
(
c
+
3
)
then what is the value of
a
+
b
+
c
a+b+c
a
+
b
+
c
?
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