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2006 IMC
5
IMC 2006, problem 5, day 2
IMC 2006, problem 5, day 2
Source:
July 25, 2006
algebra
polynomial
Vieta
IMC
college contests
Problem Statement
Show that there are an infinity of integer numbers
m
,
n
m,n
m
,
n
, with
g
c
d
(
m
,
n
)
=
1
gcd(m,n)=1
g
c
d
(
m
,
n
)
=
1
such that the equation
(
x
+
m
)
3
=
n
x
(x+m)^{3}=nx
(
x
+
m
)
3
=
n
x
has 3 different integer sollutions.
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