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Turkey MO (2nd round)
2004 Turkey MO (2nd round)
3
3
Part of
2004 Turkey MO (2nd round)
Problems
(1)
Turkey NMO-2004 P.3, nice problem about diophantine equation
Source:
11/19/2010
(a) Determine if exist an integer
n
n
n
such that
n
2
−
k
n^2 -k
n
2
−
k
has exactly
10
10
10
positive divisors for each
k
=
1
,
2
,
3.
k = 1, 2, 3.
k
=
1
,
2
,
3.
(b) Show that the number of positive divisors of
n
2
−
4
n^2 -4
n
2
−
4
is not
10
10
10
for any integer
n
.
n.
n
.
number theory proposed
number theory