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Lusophon Mathematical Olympiad
2019 Lusophon Mathematical Olympiad
2
2
Part of
2019 Lusophon Mathematical Olympiad
Problems
(1)
infinite triples a,b,c such a+b +c=n, ax^2 + bx + c = 0 has rational roots
Source: Lusophon 2019 CPLP P2
12/31/2019
Prove that for every
n
n
n
nonzero integer , there are infinite triples of nonzero integers
a
,
b
a, b
a
,
b
and
c
c
c
that satisfy the conditions: 1.
a
+
b
+
c
=
n
a + b + c = n
a
+
b
+
c
=
n
2.
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
has rational roots.
algebra
trinomial
Rational roots