MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2000 Korea Junior Math Olympiad
5
5
Part of
2000 Korea Junior Math Olympiad
Problems
(1)
a=2(A)99…99(B)(C)
Source: 2000 KJMO
6/29/2024
a
a
a
is a
2000
2000
2000
digit natural number of the form
a
=
2
(
A
)
99
…
99
(
B
)
(
C
)
a=2(A)99…99(B)(C)
a
=
2
(
A
)
99
…
99
(
B
)
(
C
)
expressed in base
10
10
10
.
a
a
a
is not a multiple of
10
10
10
, and
2
(
A
)
+
(
B
)
(
C
)
=
99
2(A)+(B)(C)=99
2
(
A
)
+
(
B
)
(
C
)
=
99
.
a
=
2899..9971
a=2899..9971
a
=
2899..9971
is a possible example of
a
a
a
.
b
b
b
is a number you earn when you write the digits of
a
a
a
in a reverse order(Writing the digits of some number in a reverse order means like reordering
1234
1234
1234
into
4321
4321
4321
). Find every positive integer
a
a
a
that makes
a
b
ab
ab
a square number.
number theory
Digits