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International Contests
Tournament Of Towns
1992 Tournament Of Towns
(345) 3
(345) 3
Part of
1992 Tournament Of Towns
Problems
(1)
TOT 345 1992 Autumn A J3 (P-Q)(x), P(x), (P+Q)(x) re squares of polynomials
Source:
6/10/2024
Do there exist two polynomials
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
with integer coefficients such that
(
P
−
Q
)
(
x
)
,
P
(
x
)
a
n
d
(
P
+
Q
)
(
x
)
(P-Q)(x), \,\,\,\, P(x) \,\,\,\, and \,\,\,\,(P+Q)(x)
(
P
−
Q
)
(
x
)
,
P
(
x
)
an
d
(
P
+
Q
)
(
x
)
are squares of polynomials (and
Q
Q
Q
is not equal to
c
P
cP
c
P
, where
c
c
c
is a real number)?(V Prasolov)
algebra
polynomial