# Math Help - Solving Modulars

1. ## Solving Modulars

Need Help with this
251^1001 (mod 101)

2. Originally Posted by dylanx5
Need Help with this
251^1001 (mod 101)
$251^{1001}=(251^{100})^{10}251^1$ but according Fermat's theorem $251^{100}$ in $Z_{101}$ is $1^{100}$ so you have that $251^{1001}$ in $Z_{101}$ is $251\bmod 101 =49$

3. thanks a lot

4. Originally Posted by andreas
$251^{1001}=(251^{100})^{10}251^1$ but according Fermat's theorem $251^{100}$ in $Z_{101}$ is $1^{100}$ so you have that $251^{1001}$ in $Z_{101}$ is $251\bmod 101 =49$

what does this symbol mean though ( $Z_{101}$) in literal terms. is it to base 101??

5. it means set of integers from +-(0 to 100). Another words all possible remainders after division by 101