Using sagemath"s jupyter notebook language code solve the following:

a$)$ You can use the function primes$(a,b)$ to find all prime numbers $p$ such that $(a,b)677?kp{k}^{p}pap.If$ you want $to$ put these primes $in$ a list, you can use the

command list$(primes(a,b).$ Create a list called $lis{t}_o{f}_p$rimes that contains all the prime numbers between $15$ and $1000.$ How many numbers are

$in$ this list? What $is$ the $12th$ number $in$ this list $(remember,$ this $is$ the number with index $11).$ What $is$ the index $of$ the prime $677?$

$b)$ Set $ktobe$ a random integer between $2$ and $16.$ For each prime $plis{t}_o{f}_p$rimes Compute the remainder $we$ get from the Euclidean division $of{k}^{p}by$

$p,$ and put these values into a list. What $do$ you notice?

Remark: $If$ you $do$ everything correctly, then what you will observe $is$ a consequence $of$ "Fermat's Little Theorem".