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Problems
Contests
International Contests
IMO Longlists
1978 IMO Longlists
39
39
Part of
1978 IMO Longlists
Problems
(1)
Prove that A+B+1 is a perfect square
Source:
10/30/2010
A
A
A
is a
2
m
2m
2
m
-digit positive integer each of whose digits is
1
1
1
.
B
B
B
is an
m
m
m
-digit positive integer each of whose digits is
4
4
4
. Prove that
A
+
B
+
1
A+B +1
A
+
B
+
1
is a perfect square.
number theory proposed
number theory