How does one determine modulo without a calculator in cases like this: $$15^7 - 13^5(\mod14)$$ Normally I would simply divide what is given by the modulo number and take the decimal output and times it by the modulo number. How can I work out $15^7 - 13^5(mod14)$ without the use of a calculator?
Now what I am thinking is: $$15 \cong 1 \mod 14 $$ $$15^7 \cong 1 \mod 14$$ $$13 \cong -1 \mod 14$$ $$13^2 \cong 1 \mod 14$$ $$13^5 \cong -1 \mod 14$$ $$[15^7 - 13^5(\mod 14)] = 1 (\mod 14) + 1 (\mod 14) = 2\mod 14$$ Is that right?