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Switzerland Team Selection Test
2003 Switzerland Team Selection Test
7
7
Part of
2003 Switzerland Team Selection Test
Problems
(1)
|Q(p_1)| = |Q(p_2)| = |Q(p_3)| = 11 , integer trinomials
Source: Switzerland - Swiss TST 2003 p7
2/18/2020
Find all polynomials
Q
(
x
)
=
a
x
2
+
b
x
+
c
Q(x)= ax^2+bx+c
Q
(
x
)
=
a
x
2
+
b
x
+
c
with integer coefficients for which there exist three different prime numbers
p
1
,
p
2
,
p
3
p_1, p_2, p_3
p
1
,
p
2
,
p
3
such that
∣
Q
(
p
1
)
∣
=
∣
Q
(
p
2
)
∣
=
∣
Q
(
p
3
)
∣
=
11
|Q(p_1)| = |Q(p_2)| = |Q(p_3)| = 11
∣
Q
(
p
1
)
∣
=
∣
Q
(
p
2
)
∣
=
∣
Q
(
p
3
)
∣
=
11
.
trinomial
polynomial
quadratic polynomial
algebra