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National and Regional Contests
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South East Mathematical Olympiad
2010 South East Mathematical Olympiad
1
2010 SMO
2010 SMO
Source:
November 1, 2010
quadratics
algebra
number theory unsolved
number theory
Problem Statement
Let
a
,
b
,
c
∈
{
0
,
1
,
2
,
⋯
,
9
}
a,b,c\in\{0,1,2,\cdots,9\}
a
,
b
,
c
∈
{
0
,
1
,
2
,
⋯
,
9
}
.The quadratic equation
a
x
2
+
b
x
+
c
=
0
ax^2+bx+c=0
a
x
2
+
b
x
+
c
=
0
has a rational root. Prove that the three-digit number
a
b
c
abc
ab
c
is not a prime number.
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