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National and Regional Contests
Romania Contests
Romania National Olympiad
1996 Romania National Olympiad
4
not hard but a cute
not hard but a cute
Source: Romani 1996
August 23, 2005
number theory
Problem Statement
Let
a
,
b
,
c
∈
Z
a,b,c\in Z
a
,
b
,
c
∈
Z
and
a
a
a
be the even number and
b
b
b
be the odd number. Show that for every integer
n
n
n
there exist one positive integer
x
x
x
such that
2
n
∣
a
x
2
+
b
x
+
c
2^n\mid ax^2+bx+c
2
n
∣
a
x
2
+
b
x
+
c
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