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Japan MO Finals
2003 Japan MO Finals
2
2
Part of
2003 Japan MO Finals
Problems
(1)
digits reversed
Source: Japanese MO 2003, Problem 2
4/20/2007
We have two distinct positive integers
a
,
b
a,b
a
,
b
with
a
∣
b
a|b
a
∣
b
. Each of
a
,
b
a,b
a
,
b
consists of
2
n
2n
2
n
decimal digits. The first
n
n
n
digits of
a
a
a
are identical to the last
n
n
n
digits of
b
b
b
, and vice versa. Determine
a
,
b
a,b
a
,
b
.
algebra
polynomial
number theory unsolved
number theory