a certain number of cats eats a certain number of mice over a period of several days.each cat eats the same number of mice .which is greater than the number of cats.if there are atleast 3 cats and the total number of mice eaten is 999919,how many cats were there?

Question

a certain number of cats eats  a certain number of mice over a period of several days.each cat eats the same number of mice .which is greater than the number of cats.if there are atleast 3 cats and the total number of mice eaten is 999919,how many cats were there?

anonymous · Answer

Let c be the number of cats and m be the number of mice eaten per cat respectively.
c*m = 999919

999919 = 991*1009 (compliments of Mathematica's function, FactorInteger. )$$(3\leq c \&\& c<m) $$c = 991 and m = 1009

There were 991 cats eating 1009 mice/cat.