Study Guide · Chapter 8
5. Finding the Unit Digit of Powers (Cyclicity Method)
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Figure: Unit-digit cycles for base 3 and base 7 — the cycle repeats forever.
Every digit, when repeatedly raised to powers 1, 2, 3, 4, …, produces unit digits that repeat in a fixed cycle. Memorising these cycles lets you find the unit digit of even a 500-digit exponent in seconds.
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