In chemistry, we came across an equation as follows:


We were supposed to assume that this implied that


Is there any mathematical reason why this holds true, or is it just a result that usually (but not always) holds true. All the $6$ variables mentioned are small positive integers (small would mean less than $100$ for sure).

  • $\begingroup$ Infinitely many solutions. And not only these. math.stackexchange.com/questions/153603/… $\endgroup$ – individ May 28 '16 at 11:36
  • $\begingroup$ Not always. Take $Z_1=5,Z_2=1,n_1=48,n_2=36,n_3=16,n_4=9$. $\endgroup$ – mathlove May 28 '16 at 11:53
  • $\begingroup$ @individ If the variables are smaller than 100 and greater than 1, surely there are not infinitely many solutions. $\endgroup$ – YoTengoUnLCD May 28 '16 at 11:57

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