Eve and Martti have a whole number of euros.

Martti said to Eve: "If you give me three euros, so I have n times the money compared to you."
Eve in turn said to Martti: "If you give me n euros then I have triple the amount of money compared to you".

Suppose, that both claims are valid. What values can a positive integer n get?

(In reply to A possible generalization by Math Man)

     n     M     E     m

     2    11     3     1

     1     7    10     2
     2     6     4     2
     3     7     2     2

     1     5    11     3
     2     5     7     3
     3     6     6     3
     7    11     5     3

     1     4    16     5
     8    11    23     5

     3     5    23     7

     2     4    24     8
     5     7    36     8

from

for a= 1:50
for n=0:1000
 m= (-a-n^2*a - n^2 - n*a)/(1-n*a);
 e=a*m-4*n;
 if m==floor(m)&&e==floor(e)&&n>0&&m>=0&&e>=0
  disp([n,m,e,a])
 end
end
end

Posted by Charlie on 2020-10-29 10:30:24