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Canadian Open Math Challenge
2017 Canadian Open Math Challenge
B4
B4
Part of
2017 Canadian Open Math Challenge
Problems
(1)
2017 COMC B4
Source:
10/12/2018
Source: 2017 Canadian Open Math Challenge, Problem B4 —-- Numbers
a
a
a
,
b
b
b
and
c
c
c
form an arithmetic sequence if
b
−
a
=
c
−
b
b - a = c - b
b
−
a
=
c
−
b
. Let
a
a
a
,
b
b
b
,
c
c
c
be positive integers forming an arithmetic sequence with
a
<
b
<
c
a < b < c
a
<
b
<
c
. Let
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax2 + bx + c
f
(
x
)
=
a
x
2
+
b
x
+
c
. Two distinct real numbers
r
r
r
and
s
s
s
satisfy
f
(
r
)
=
s
f(r) = s
f
(
r
)
=
s
and
f
(
s
)
=
r
f(s) = r
f
(
s
)
=
r
. If
r
s
=
2017
rs = 2017
rs
=
2017
, determine the smallest possible value of
a
a
a
.
Comc
2017 COMC