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All-Russian Olympiad
1986 All Soviet Union Mathematical Olympiad
430
430
Part of
1986 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 430 All Soviet Union MO 1986 a^2 + b = c, find three no with equal digits
Source:
8/6/2019
The decimal notation of three natural numbers consists of equal digits:
n
n
n
digits
x
x
x
for
a
a
a
,
n
n
n
digits
y
y
y
for
b
b
b
and
2
n
2n
2
n
digits
z
z
z
for
c
c
c
. For every
n
>
1
n > 1
n
>
1
find all the possible triples of digits
x
,
y
,
z
x,y,z
x
,
y
,
z
such, that
a
2
+
b
=
c
a^2 + b = c
a
2
+
b
=
c
Digits
number theory