Find all positive integer solutions of the equation $1650_x = 1131_3$$_y$ where $x$ and $3y$ are the bases of the numbers on the two sides.
I have this example in my book but have never come across an equation like this and I can't seem to find anything about these online.
Am I correct to by starting with
$1650_x = 1*x^3 + 6*x^2 +5*x^1 + 0*x^0 = x^3+6x^2+5x$
$1131_3$$_y = (3y)^3 + (3y)^2 + 9y + 1$
If so, where do I go from here? If not, than I am lost. Any help would be appreciated. Thanks.
Hint: What are the residues of $$1650_x = x^3+6x^2+5x = x(x+1)(x+5)$$ and $$1131_{3y} = (3y)^3+(3y)^2+3(3y)+1 = 3(9y^3+3y^2+3y)+1$$ modulo $3$?