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National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2017 Saudi Arabia Pre-TST + Training Tests
4
4
Part of
2017 Saudi Arabia Pre-TST + Training Tests
Problems
(1)
n roots of polynomial form an arithmetic sequence
Source: 2017 Saudi Arabia IMO Training Test p4
9/4/2020
Does there exist an integer
n
≥
3
n \ge 3
n
≥
3
and an arithmetic sequence
a
0
,
a
1
,
.
.
.
,
a
n
a_0, a_1, ... , a_n
a
0
,
a
1
,
...
,
a
n
such that the polynomial
a
n
x
n
+
.
.
.
+
a
1
x
+
a
0
a_nx^n +... + a_1x + a_0
a
n
x
n
+
...
+
a
1
x
+
a
0
has
n
n
n
roots which also form an arithmetic sequence?
arithmetic sequence
algebra
polynomial