Use the result of Exercise 7 and the method of successive differences to find the first eight octagonal numbers. Then divide each by 4 and record the remainder. What is the pattern obtained?
(Reference Exercise 7)
Consider the following equations, where the left side of each is an octagonal number.
1 = 1
8 = 1 + 7
21 = 1 + 7 + 13
40 = 1 + 7 + 13 + 19
Use the pattern established on the right sides to predict the next octagonal number. What is the next equation in the list?
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