(4.4.45) Proving Divisibility: If n Ends in Five, Then 5 Divides n

In this tutorial, I guide you through a proof of a universally quantified statement: if n is any non-negative integer whose decimal representation ends in five, then 5 divides it. I start by establishing an arbitrary instantiation for n, a non-negative integer ending in five. I then rewrite n using different factors, factoring out a five and showing how the remaining factors form an integer, denoted as M. Since n equals 5 times M, by definition, 5 divides n. This tutorial offers a detailed look at the process of proving divisibility through logical reasoning and mathematical definitions.

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