For the eqn. ab + c = t where a,b,c are three consecutive numbers. show that "t" will never be a perfect power?

How we can write 0×2 & 2×0 both in a successive addition way separately?

For the eqn. ax+b=y^n, where a,b,x are any +ve integers & y & n are distinct odd primes, the only integral solutions for y^n is y=b & n=a?