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Vietnam Contests
Vietnam National Olympiad
1974 Vietnam National Olympiad
1
1
Part of
1974 Vietnam National Olympiad
Problems
(1)
a_{2n}-ba_n is square, if a_n is positive integer with n digits all =1, b digit
Source: Vietnamese MO (VMO) 1974
8/20/2018
Find all positive integers
n
n
n
and
b
b
b
with
0
<
b
<
10
0 < b < 10
0
<
b
<
10
such that if
a
n
a_n
a
n
is the positive integer with
n
n
n
digits, all of them
1
1
1
, then
a
2
n
−
b
a
n
a_{2n} - b a_n
a
2
n
−
b
a
n
is a square.
number theory
Digits
positive integer