How many pairs of positive integers m,n satisfies (1/m)+(4/n)=1/12, where n is an odd integer less than 60.

• 1/m = 1/12 - 4/n
  
  Since m is positive,
  n must be greater than 48.
  Possible odd values of n such that 48 < n < 60 are 49, 51, 53, 55, 57 and 59 of which only 49, 51 and 57 give integral values of m.
  So,there are 3 solutions
  
  
• 12 years agoHelpfull: Yes(15) No(0)
• The given condition is 1/m + 4/n = 1/12
  = (n + 4m)12 = mn
  = 12n + 48m = mn
  = mn – 12n + 48m = 0
  = n(m – 12) + 48 (m – 12) = 12 * 48 = 576
  = (m – 12) (n + 48) = 576
  Now, the prime factors of 576 which satisfy m = 12n / (n – 48) are 49, 51, and 57.
  
  so totally three prime factors
  
• 12 years agoHelpfull: Yes(9) No(1)