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Kvant 2019
M2575
M2575
Part of
Kvant 2019
Problems
(1)
Polynomial with coefficients -1 or 1
Source: Kvant Magazine No. 9 2019 M2575
3/14/2023
Let
t
∈
(
1
,
2
)
t\in (1,2)
t
∈
(
1
,
2
)
. Show that there exists a polynomial
P
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
.
.
.
+
a
1
x
+
a
0
P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0
P
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
...
+
a
1
x
+
a
0
with the coefficients in
{
1
,
−
1
}
\{1,-1\}
{
1
,
−
1
}
such that
∣
P
(
t
)
−
2019
∣
⩽
1.
\left|P(t)-2019\right| \leqslant 1.
∣
P
(
t
)
−
2019
∣
⩽
1.
Proposed by N. Safaei (Iran)
algebra
polynomial
Kvant