How many ordered pairs of (m,n) integers satisfy `(m)/(12)=(12)/(n)`?

The number of positive integer pairs (m,n) where n is odd,that satisfy (1)/(m)+(4)/(n)=(1)/(12) is

How many pairs of positive integers m and n satisfy the equation (1)/(m) +(4)/(n) =(1)/(12) where n is an odd integer less than 60?

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

Given that sum_(k=1)^(35)sin5k^(@)=tan((m)/(n))^(@), where m and n are relatively prime positive integers that satisfy ((m)/(n))^(@)<90^(@), then m+n is equal to

If m and n are integers satisfying (m-8)(m-10)=2^(n) ,then the number of ordered pairs (m,n) is

If m and n are positive integers such that (m-n)^(2)=(4mn)/((m+n-1)) , then how many pairs (m, n) are possible?