When, in algebra, two letters are written next to each other as a term, such as m and n becoming mn, it means they are multiplied. So mn is a shorter way of writing "m times n" or "m x n"
Therefore, when m = 1 and n = 1, mn = 1 x 1 = 1
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m = n/(n-1)
Given m equals 3 and n equals 1 then m3n3 equals?m3n3 = m*3*n*3 = 3*3*1*3 = [ 27 ]
Let the integers be m and n.∴ By the condition given in the question,m + n - mn = 72∴ m + n - mn = 71 + 1∴ m + n - mn - 1 = 71∴ (m - 1)(1 - n) = 71∴ (m - 1)(1 - n) = 1 × 71 = 71 × 1 = (-1) × (-71) = (-71) × (-1)Case 1:m - 1 = 1 and 1 - n = 71∴ (m, n) = (2, -70)Case 2:m - 1 = 71 and 1 - n = 1∴ (m , n) = (72, 0)This case is inadmissible as m, n are non zero integers.Case 3:m - 1 = -1 and 1 - n = -71∴ (m , n) = (0, 72)This case is inadmissible as m, n are non zero integers.Case 4:m - 1 = -71 and 1 - n = -1∴ (m, n) = (-70, 2)But as the given expression is symmetric, therefore, (2, -70) and (-70, 2) cannot be considered two different pairs.∴ We get only one solution.
mn - 4m - 5n + 20 = m(n - 4) - 5(n - 4) = (n - 4)(m - 5)
m = 24