Hi. I've been practicing solving equations these days and today, I found this problem. Here it is.

Solve this equation. (a, b, c, d, e are all natural numbers)

$\displaystyle abcde-a=357^{400}$

$\displaystyle abcde-b=359^{410}$

$\displaystyle abcde-c=361^{420}$

$\displaystyle abcde-d=363^{430}$

$\displaystyle abcde-e=365^{440}$

Well, I can solve an equation with two or three variables but

what should I do if the number of variables are more than three?