Proof for set of 15 values that have property a−c=d−b

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I am pretty sure (please correct me if this is untrue), that in a set of 15 different values, ranging from integers (1-100), that there are four numbers, a,b,c,d such that a−c=d−b.

I have tried to understand why this is true, but just cannot wrap my head around it, any guidance on why this is the case (or if it isn't) would be much appreciated! Thanks!