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2022 BMT
17
BMT 2022 Guts #17
BMT 2022 Guts #17
Source:
August 31, 2023
algebra
system of equations
number theory
Problem Statement
Compute the number of ordered triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of integers between
−
100
-100
−
100
and
100
100
100
inclusive satisfying the simultaneous equations
a
3
−
2
a
=
a
b
c
−
b
−
c
a^3 - 2a = abc - b - c
a
3
−
2
a
=
ab
c
−
b
−
c
b
3
−
2
b
=
b
c
a
−
c
−
a
b^3 - 2b = bca - c - a
b
3
−
2
b
=
b
c
a
−
c
−
a
c
3
−
2
c
=
c
a
b
−
a
−
b
.
c^3 - 2c = cab - a - b.
c
3
−
2
c
=
c
ab
−
a
−
b
.
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