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2009 JBMO Shortlist
1
a + b + c = 15 , (a - 3)^3 + (b - 5)^3 + (c -7)^3 = 540
a + b + c = 15 , (a - 3)^3 + (b - 5)^3 + (c -7)^3 = 540
Source: JBMO 2009 Shortlist A1
October 14, 2017
JBMO
algebra
system of equations
Problem Statement
Determine all integers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfying identities:
a
+
b
+
c
=
15
a + b + c = 15
a
+
b
+
c
=
15
(
a
−
3
)
3
+
(
b
−
5
)
3
+
(
c
−
7
)
3
=
540
(a - 3)^3 + (b - 5)^3 + (c -7)^3 = 540
(
a
−
3
)
3
+
(
b
−
5
)
3
+
(
c
−
7
)
3
=
540
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