solving this diophantine equation on sagemath
Consider the diophantine equation:
x*y*(y + 2(6*n + 3 + x)) == 36*n^3 + 54*n^2 + 27*n - 4, where x,y,n are nonzero integers, what commands do I run on sagemath to get specifically integer values to my question?
There is no generic function that can solve such equations. However, if you fix value of one of the variables, you'll get an elliptic curve and there is a method to determine integral points on it.