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mcnole25/final-digits.md

Created March 18, 2025 01:28
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Table for period length of final digits for k^n.
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final-digits.md

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
5 2500 5000 1250 8 625 500 2500 2500
6 12500 50000 6250 16 3125 5000 12500 25000
7 62500 500000 31250 32 15625 50000 62500 250000
8 312500 5000000 156250 64 78125 500000 312500 2500000
9 1562500 50000000 781250 128 390625 5000000 1562500 25000000
10 7812500 500000000 3906250 256 1953125 50000000 7812500 250000000
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