MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1969 Swedish Mathematical Competition
5
5
Part of
1969 Swedish Mathematical Competition
Problems
(1)
N =a_1a_2...a_n= 0 mod 3 if a_1-a_2 + a_3 -... + (-1)^{n-1}a_n = 0 mod 3
Source: 1969 Swedish Mathematical Competition p5
3/21/2021
Let
N
=
a
1
a
2
.
.
.
a
n
N = a_1a_2...a_n
N
=
a
1
a
2
...
a
n
in binary. Show that if
a
1
−
a
2
+
a
3
−
.
.
.
+
(
−
1
)
n
−
1
a
n
=
0
a_1-a_2 + a_3 -... + (-1)^{n-1}a_n = 0
a
1
−
a
2
+
a
3
−
...
+
(
−
1
)
n
−
1
a
n
=
0
mod
3
3
3
, then
N
=
0
N = 0
N
=
0
mod
3
3
3
.
number theory
divides
divisible