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Problems
Contests
National and Regional Contests
Germany Contests
German National Olympiad
1965 German National Olympiad
5
5
Part of
1965 German National Olympiad
Problems
(1)
\sqrt{ xxx...x - yy...y}= zzz...z, for digits
Source: Germany 1965 p5
2/21/2020
Determine all triples of nonzero decimal digits
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
for which the equality
x
x
x
.
.
.
x
⏟
2
n
−
y
y
.
.
.
y
⏟
n
=
z
z
z
.
.
.
z
⏟
n
\sqrt{ \underbrace{xxx...x}_{2n}- \underbrace{yy...y}_{n}}= \underbrace{zzz...z}_{n}
2
n
xxx
...
x
−
n
yy
...
y
=
n
zzz
...
z
holds for at least two different natural numbers
n
n
n
.
Digits
number theory