Consider the sequence formed by the final decimal digits of kn. What is the period length? The table is shown below.
Example: the final digit of 2x cycles {2, 4, 8, 6, 2, 4, 8, 6, 2, 4, 8, 6...} giving it a period length of 4.
Final | 2n | 3n | 4n | 5n | 6n | 7n | 8n | 9n |
---|---|---|---|---|---|---|---|---|
1 | 4 | 4 | 2 | 1 | 1 | 4 | 4 | 2 |
2 | 20 | 20 | 10 | 1 | 5 | 4 | 20 | 10 |
3 | 100 | 100 | 50 | 2 | 25 | 20 | 100 | 50 |
4 | 500 | 500 | 250 | 4 | 125 | 100 | 500 | 250 |