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IMO Longlists
1977 IMO Longlists
12
12
Part of
1977 IMO Longlists
Problems
(1)
Determine the set T - [ILL 1977]
Source:
1/11/2011
Let
z
z
z
be an integer
>
1
> 1
>
1
and let
M
M
M
be the set of all numbers of the form
z
k
=
1
+
z
+
⋯
+
z
k
,
k
=
0
,
1
,
…
z_k = 1+z + \cdots+ z^k, \ k = 0, 1,\ldots
z
k
=
1
+
z
+
⋯
+
z
k
,
k
=
0
,
1
,
…
. Determine the set
T
T
T
of divisors of at least one of the numbers
z
k
z_k
z
k
from
M
.
M.
M
.
modular arithmetic
number theory
relatively prime
number theory proposed