Question

If m+n=mn-5, then the maximum number of ordered pairs of (m,n) for every m,n is a natural number.

Answer 1

Hi

Thank you for asking the question

Given:

M + n = m*n -5

m= (n+5)/ (n-1)
i.e. m= 1 + 6/ (n-1)

Hence (n-1) cannot be 0 and cannot be more than 6 and has to be a factor of 6...For example. n-1 can take values of 1,2,3,6
therefore, n can take values of 2,3,4,7 and corresponding values of m are 7,4,3,2
i.e. the 4 ordered pairs are (7,2) , (4,3) , (3,4), (2,7).