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1992 IMO Longlists
6
6
Part of
1992 IMO Longlists
Problems
(1)
Probablity for a modular equation
Source:
9/1/2010
Suppose that n numbers
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, . . . , x_n
x
1
,
x
2
,
...
,
x
n
are chosen randomly from the set
{
1
,
2
,
3
,
4
,
5
}
\{1, 2, 3, 4, 5\}
{
1
,
2
,
3
,
4
,
5
}
. Prove that the probability that
x
1
2
+
x
2
2
+
⋯
+
x
n
2
≡
0
(
m
o
d
5
)
x_1^2+ x_2^2 +\cdots+ x_n^2 \equiv 0 \pmod 5
x
1
2
+
x
2
2
+
⋯
+
x
n
2
≡
0
(
mod
5
)
is at least
1
5
.
\frac 15.
5
1
.
probability
modular arithmetic
function
algebra
combinatorics
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