Thread: proof for equation with no solution

How to prove that there is no solution for this equation in natural numbers:

Did you check the equation mod 2, 3, 5? There, you can analyse all cases, and maybe no case can satisfy the equation - in this case, it is impossible to satisfy your equation.

What if i take mod 3 ,how is that show that there is no solution ?

Mod 3 doesn't help, because the LHS is 1 (mod 3) and can also be congruent to 1 (mod 3).

However, mod 9 gives a nice solution. Try using mod 9.