Discussion
The digit in the unit's place of the number \((47)^{25} - 1\) must be :
Answer: C
The unit's digit is 6.
The unit's digit of \(47^{25}\) depends only on the unit's digit 7. Powers of 7 end in a repeating cycle of four: 7, 9, 3, 1. Since \(25 = 4 \times 6 + 1\), the 25th power is in position 1 of the cycle and ends in 7.
Subtracting 1 gives a number ending in \(7 - 1 = 6\).
7 is the unit's digit of \(47^{25}\) itself, before the 1 is subtracted, and 1 and 8 come from using the wrong position in the cycle.
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