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National and Regional Contests
South Africa Contests
South Africa National Olympiad
2004 South africa National Olympiad
1
1
Part of
2004 South africa National Olympiad
Problems
(1)
GCD of two numbers consisting of ones
Source: South African MO 2004 Q1
5/27/2012
Let
a
=
1111
…
1111
a=1111\dots1111
a
=
1111
…
1111
and
b
=
1111
…
1111
b=1111\dots1111
b
=
1111
…
1111
where
a
a
a
has forty ones and
b
b
b
has twelve ones. Determine the greatest common divisor of
a
a
a
and
b
b
b
.
number theory
greatest common divisor
algorithm
number theory unsolved