Exercises 48 and 49 are specific cases of the following: When the numbers in the sequence of n-agonal numbers are divided by n, the sequence of remainders obtained is a repeating sequence. Verify this for n = 5 and n = 6.
(Reference Exercise 49)
Repeat Exercise 48, but instead use square numbers and divide by 4. What pattern is determined?
(Reference Exercise 48)
Divide the first triangular number by 3 and record the remainder. Divide the second triangular number by 3 and record the remainder. Repeat this procedure several more times. Do you notice a pattern?
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