Consider p , m , n and c as known integers and a and b are variables.
Let the equation be :
pab = ma + nb + c
pab - nb = ma + c
pb (a - n/p) = m(a - n/p + n/p) + c
pb (a - n/p) = m(a - n/p) + mn/p + c
(a - n/p) (pb - m) = (mn + pc) / p
{(pa - n) / p } (pb - m) = (mn + pc ) / p
(pa - n) (pb - m) / p = (mn + pc ) / p
Multiplying both sides by non zero p
Result : (pa - n) (pb - m) = mn + pc
Note : This result must be memorised.