MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2023-24 IOQM India
1
1
Part of
2023-24 IOQM India
Problems
(1)
IOQM 2023-24 P-1
Source:
9/3/2023
Let
n
n
n
be a positive integer such that
1
≤
n
≤
1000
1 \leq n \leq 1000
1
≤
n
≤
1000
. Let
M
n
M_n
M
n
be the number of integers in the set
X
n
=
{
4
n
+
1
,
4
n
+
2
,
…
,
4
n
+
1000
}
X_n=\{\sqrt{4 n+1}, \sqrt{4 n+2}, \ldots, \sqrt{4 n+1000}\}
X
n
=
{
4
n
+
1
,
4
n
+
2
,
…
,
4
n
+
1000
}
. Let
a
=
max
{
M
n
:
1
≤
n
≤
1000
}
, and
b
=
min
{
M
n
:
1
≤
n
≤
1000
}
.
a=\max \left\{M_n: 1 \leq n \leq 1000\right\} \text {, and } b=\min \left\{M_n: 1 \leq n \leq 1000\right\} \text {. }
a
=
max
{
M
n
:
1
≤
n
≤
1000
}
, and
b
=
min
{
M
n
:
1
≤
n
≤
1000
}
.
Find
a
−
b
a-b
a
−
b
.