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1972 Bulgaria National Olympiad
Problem 1
Problem 1
Part of
1972 Bulgaria National Olympiad
Problems
(1)
9|(x+a)(x+b)(x+c)-x^3-1 doesn't hold for some x and all a,b,c
Source: Bulgaria 1972 P1
6/21/2021
Prove that there are don't exist integers
a
,
b
,
c
a,b,c
a
,
b
,
c
such that for every integer
x
x
x
the number
A
=
(
x
+
a
)
(
x
+
b
)
(
x
+
c
)
−
x
3
−
1
A=(x+a)(x+b)(x+c)-x^3-1
A
=
(
x
+
a
)
(
x
+
b
)
(
x
+
c
)
−
x
3
−
1
is divisible by
9
9
9
.I. Tonov
number theory