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2000 Japan MO Finals
1
1
Part of
2000 Japan MO Finals
Problems
(1)
Sequence of rational points P_i forming unit distances
Source: Japanese MO Finals 2000
2/10/2011
Consider the points
O
(
0
,
0
)
O(0,0)
O
(
0
,
0
)
and
A
(
0
,
1
/
2
)
A(0,1/ 2)
A
(
0
,
1/2
)
on the coordinate plane. Prove that there is no finite sequence of rational points
P
1
,
P
2
,
…
,
P
n
P_1,P_2,\ldots ,P_n
P
1
,
P
2
,
…
,
P
n
in the plane such that
O
P
1
=
P
1
P
2
=
…
=
P
n
−
1
P
n
=
P
n
A
=
1
OP_1=P_1P_2=\ldots =P_{n-1}P_n=P_nA=1
O
P
1
=
P
1
P
2
=
…
=
P
n
−
1
P
n
=
P
n
A
=
1
analytic geometry
number theory unsolved
number theory