Modular arithmetic and powers

Question

Suppose: $$a=(5^4 \pmod 7)^3 \pmod {13}$$

How would you go about solving this? The only thing I came up with is an ugly polynomial: $a=13k+7l^3+5^{12}$ but this doesn't tell me much. Any starting point would be great.

hint: $(5^4 \pmod 7)=2$ – Salech Alhasov Dec 06 '13 at 03:22 — Salech Alhasov, Dec 06 '13 at 03:22

score 0 · Accepted Answer · edited Dec 06 '13 at 03:30

0

$$5^2\mod 7 = -3$$ $$5^4 \mod 7 = 2$$. $$2^3=8$$.

edited Dec 06 '13 at 03:30

Salech Alhasov

6,780
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answered Dec 06 '13 at 03:28

Carl Love

1,193

Modular arithmetic and powers

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