Question

if 3^100-2^100 is divided by 11, what is the reminder
can any1 explain

Answer 1

i have an answer but it is not snappy so maybe there is a better way to do it

Answer 2

the answer is 0, i.e. 11 divides the number. it is because one of the factors of
\[x^{100}-y^{100}\] is
\[(x^4-x^3 y+x^2 y^2-x y^3+y^4) \] and if you replace x by 2 and y by 2 you get 55

Answer 3

Mathematica can handle unlimited precision numbers.\[\text{Mod}\left[3^{100}-2^{100},11\right]=0 \]