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All-Russian Olympiad
1962 All-Soviet Union Olympiad
4
Cubic with Integer Coefficients
Cubic with Integer Coefficients
Source: 1962 All-Soviet Union Olympiad
January 15, 2018
algebra
Russia
Problem Statement
Prove that there are no integers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
such that the polynomial
a
x
3
+
b
x
2
+
c
x
+
d
ax^3+bx^2+cx+d
a
x
3
+
b
x
2
+
c
x
+
d
equals
1
1
1
at
x
=
19
x=19
x
=
19
and
2
2
2
at
x
=
62
x=62
x
=
62
.
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