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Rich and poor integers

Source: Benelux MO 2019 P4

April 28, 2019
number theoryBxMO

Problem Statement

An integer m>1m>1 is rich if for any positive integer nn, there exist positive integers x,y,zx,y,z such that n=mx2−y2−z2n=mx^2-y^2-z^2. An integer m>1m>1 is poor if it is not rich.
[*]Find a poor integer.[/*] [*]Find a rich integer.[/*]
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