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Benelux
2019 Benelux
4
4
Part of
2019 Benelux
Problems
(1)
Rich and poor integers
Source: Benelux MO 2019 P4
4/28/2019
An integer
m
>
1
m>1
m
>
1
is rich if for any positive integer
n
n
n
, there exist positive integers
x
,
y
,
z
x,y,z
x
,
y
,
z
such that
n
=
m
x
2
−
y
2
−
z
2
n=mx^2-y^2-z^2
n
=
m
x
2
−
y
2
−
z
2
. An integer
m
>
1
m>1
m
>
1
is poor if it is not rich.[*]Find a poor integer.[/*] [*]Find a rich integer.[/*]
number theory
BxMO