Abby notices that for the first twenty perfect​ squares, each square is either a multiple of​ 5, one less than a multiple of​ 5, or one more than a multiple of 5. She writes the following statement. If n is a natural​ number, then n can be written as 5k​1, ​5k, or 5k​1, where k is a whole number.
What type of statement did Abby​ make? Has she shown that her statement is true for all values of​ n? Explain.
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400