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2006 Japan MO Finals
2
2
Part of
2006 Japan MO Finals
Problems
(1)
Japan mathematical olympiad finals 2006, problem 2
Source:
3/3/2006
Determine all integers
k
k
k
for which there exist infinitely the pairs of integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
satisfying the following equation.
(
a
2
−
k
)
(
b
2
−
k
)
=
c
2
−
k
.
(a^2-k)(b^2-k)=c^2-k.
(
a
2
−
k
)
(
b
2
−
k
)
=
c
2
−
k
.
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