Proving a language is non-regular using the Pumping Lemma for non-binary strings

Question

I am unsure of how to prove this language is non-regular. I do not even know where to start to develop a string that would prove the language is non-regular by contradiction. Any help would be appreciated.

I understand that the string has to have a length greater than the pumping length of L. What does that even mean in this context of such a vast alphabet?

I imagine I have to choose a string that fits the properties:

must be in the form of the expression a+b=c no leading zeros in a,b,c the expression on the left must equal the value on the right But I do not know what string would fit all these properties but also provides a contradiction in the proof.

My Attempt:

Answer 1

You have demonstrated a pretty good understanding of the pumping lemma for regular languages. Your proof is clean and correct. (That mino typo, $xy^{iz}$ where $z$ should not be in the superscript, could be ignored by a human reader.)

Here is a minor suggestion. You can just use a specific string such as $1^p+2^p=3^p$, instead of a more general one $a^p+b^p=c^p$. Your proof will become easier to write and easier to understand.