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Swedish Mathematical Competition
1984 Swedish Mathematical Competition
4
4
Part of
1984 Swedish Mathematical Competition
Problems
(1)
(x^2 - px+q)(x^2 -qx+ p) has pos. integer roots
Source: 1984 Swedish Mathematical Competition p4
3/28/2021
Find all positive integers
p
p
p
and
q
q
q
such that all the roots of the polynomial
(
x
2
−
p
x
+
q
)
(
x
2
−
q
x
+
p
)
(x^2 - px+q)(x^2 -qx+ p)
(
x
2
−
p
x
+
q
)
(
x
2
−
q
x
+
p
)
are positive integers.
algebra
polynomial