On a certain diophantine equation

Extract

The unit of currency on Mars is the zonk, which consists of a whole number of zinks. An enlightened, though somewhat green, government recently decided to revamp the taxation system, which at the time was manifestly unfair to male Martians as it required them to pay less tax than females. (Martians are very unselfish and feel aggrieved if they are better off than other Martians.)

Previously, only females had had to pay ‘Population Tax’, each having to pay a certain number of zonks, that number being the total number of males. (The idea was to encourage polygamous marriages.) After the change, all Martians, male and female, were to pay Population Tax, which was to be a certain number of zinks, that number being the total number of males and females.