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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2010 All-Russian Olympiad Regional Round
11.7
11.7
Part of
2010 All-Russian Olympiad Regional Round
Problems
(1)
2 trinomials with same value at x=1234
Source: Russian Regional Olympiad 2010 11.7
8/24/2024
Integers
a
,
b
,
c
a,b,c
a
,
b
,
c
are such that the values of the trinomials
b
x
2
+
c
x
+
a
bx^2+cx+a
b
x
2
+
c
x
+
a
and
c
x
2
+
a
x
+
b
cx^2+ax+b
c
x
2
+
a
x
+
b
at
x
=
1234
x=1234
x
=
1234
coincide. Can the first trinomial at
x
=
1
x = 1
x
=
1
take the value
2009
2009
2009
?
algebra
trinomial