Recently, I was facing some problems in effectively proving the following :

Consider the alphabet Σ ={0,1,2,...,9,#}, and the language of strings of the form x#y#z, where x,y and z are strings of digit such that when viewed as numbers, satisfy the mathematical equation x+y=z.

For example, the string 123#45#168 is in this language because 123 + 45 = 168.

Is this language regular and why ?

I was trying to apply the Pumping Lemma, but am unsure of how to complete the proof. Could anyone please help ?

Recently, I was facing some problems in effectively proving the following :

Consider the alphabet Σ ={0,1,2,...,9,#}, and the language of strings of the form x#y#z, where x,y and z are strings of digit such that when viewed as numbers, satisfy the mathematical equation x+y=z.

For example, the string 123#45#168 is in this language because 123 + 45 = 168.

Is this language regular and why ?

I was trying to apply the Pumping Lemma, but am unsure of how to complete the proof. Could anyone please help ?