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a+b+c= (a-b)(b-c)(c-a) = m (mod 27) (HOMC 2015 J Q5)
a+b+c= (a-b)(b-c)(c-a) = m (mod 27) (HOMC 2015 J Q5)
Source:
August 6, 2019
number theory
modulo
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
and
m
m
m
(
0
≤
m
≤
26
0 \le m \le 26
0
≤
m
≤
26
) be integers such that
a
+
b
+
c
=
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
=
m
a + b + c = (a - b)(b- c)(c - a) = m
a
+
b
+
c
=
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
=
m
(mod
27
27
27
) then
m
m
m
is(A):
0
0
0
, (B):
1
1
1
, (C):
25
25
25
, (D):
26
26
26
(E): None of the above.
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