Aviv29 wrote:
17^27 has a units digit of:
(a) 1
(b) 2
(c) 3
(d) 7
(e) 9
\(? = \left\langle {{{17}^{27}}} \right\rangle = \left\langle {{7^{27}}} \right\rangle\)
\(\left\langle {{7^4}} \right\rangle = \left\langle {{7^2} \cdot {7^2}} \right\rangle = \left\langle {\left\langle {{7^2}} \right\rangle \cdot \left\langle {{7^2}} \right\rangle } \right\rangle = 1\)
\(\left\langle {{7^{24}}} \right\rangle = \left\langle {{7^4} \cdot {7^4} \cdot \ldots \cdot {7^4}} \right\rangle = {\left\langle {{7^4}} \right\rangle ^6} = 1\)
\(? = \left\langle {{7^{24}} \cdot {7^3}} \right\rangle = \left\langle {{7^{24}}} \right\rangle \cdot \left\langle {{7^3}} \right\rangle = 1 \cdot 3 = 3\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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