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Question Number 89454 by student work last updated on 17/Apr/20

Commented by Tony Lin last updated on 17/Apr/20

$$32mod7=4$$$${32}^{2}mod7=2$$$${32}^{3}mod7=1$$$${32}^{4}mod7=4$$$$\cdot \cdot \cdot$$$$\Rightarrow {32}^{3k+1}mod7=4$$$${32}^{3k+2}mod7=2$$$${32}^{3k}mod7=1$$$$32mod3=2$$$${32}^{2}mod3=1$$$${32}^{3}mod3=2$$$$\cdot \cdot \cdot$$$$\Rightarrow {32}^{2k+1}mod3=2$$$${32}^{2k}mod3=1$$$$\therefore {32}^{32}mod3=1$$$$\Rightarrow {32}^{{32}^{32}}mod7={32}^{3k+1}mod7=4$$

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