What is the answer to

3^46=____ (mod 8) ?

You can also do it on the web2 calc (it is on the Home page)

Mod(3^46,8)

$$\left({{\mathtt{3}}}^{{\mathtt{46}}}\right) {Mod} \left({\mathtt{8}}\right) = {\mathtt{1}}$$

You will find the answer here: http://m.wolframalpha.com/input/?i=solve+3%5E46+mod+8&x=0&y=0

3^{1} = 3 mod 8 = 3 3^{3} = 27 mod 8 = 3 3^{5} = 243 mod 8 = 3

3^{2} = 9 mod 8 = 1 3^{4} = 81 mod 8 = 1 3^{6} = 729 mod 8 = 1

So, if the exponent is even, its mod 8 value is 8 ...

and, if the exponent is add, its mode 8 value is 1 ...