Here are a series of tasks for you to attempt in Sage. You will want to reference “Mini Sage Introduction” and “Programming Basics” examples in the menu.

**Task 1. ** Write a loop that will successively square a number modulo n. Use it to compute $2^{1024} \pmod {101}$. Make it show its work, by making informative print statements at each step.

**Task 2.** Create a `while`

loop which finds the first integer greater than 202 which is square. You can use the function `is_square()`

to check if something is a square. It returns True or False.

**Task 3.** Create a function that finds the first integer greater than $n$ which is a square, and returns it. You will want to adapt the code you just created above.

Here’s a separate box for testing your function.

**Task 4.** Create a program that computes the first 100 Fibonacci numbers and places them in a list.

**Task 5.** Create a function that implements Pollard’s p-1 factorization method, on any input integer $n$. You can use Sage’s inbuilt gcd.

Here’s a separate box for testing your function.

**Task 6.** Implement the Sieve of Eratosthenes on the primes from 1 to 100.

An extra box.