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418
ASU 418 All Soviet Union MO 1986 x^2+ax+b+1 natural roots a^2+b^2 composite
ASU 418 All Soviet Union MO 1986 x^2+ax+b+1 natural roots a^2+b^2 composite
Source:
August 5, 2019
algebra
polynomial
Composite
trinomial
Problem Statement
The square polynomial
x
2
+
a
x
+
b
+
1
x^2+ax+b+1
x
2
+
a
x
+
b
+
1
has natural roots. Prove that
(
a
2
+
b
2
)
(a^2+b^2)
(
a
2
+
b
2
)
is a composite number.
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