The number of pairs (m, n) of integers such that n^2-3 m n+m-n=0 is

Step-by-step solution

(3 m+1)(3 n-1)=3 n^2-1 , so if p divides 3 n-1 , then it also divides 3 n^2-1 and hence also (3 n^2-1 )-n(3 n-1)=n-1 , and hence also (3 n-1)-3(n-1)=2 . So 3 n-1=0, 1 or 2 . But n must be an integer, so 0,1,-2 do not work. -1 gives n =0 and hence m =0 , which is a solution. 2 gives n=1 and hence m=0 , which is a solution.