Sum of Squares

Problem of the Week #17: Monday May 1st, 2023
The start of May caught me by surprise, so the decision to make this month's topic Number Theory was a bit last minute.  Please hit me with ideas if you have them.
As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems.
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a). What is the smallest whole number that cannot be expressed as the sum of the squares of two whole numbers (0, 1, 2…) if the two numbers can be equal?

b). List the first 20 whole numbers that cannot be expressed as the sum of the squares of two whole numbers.

c). List the first 10 whole numbers of the form 4k+3, where k is a whole number.  Compare this list to b).  Does this pattern continue?  Why or why not?

d). Given a whole number n, how can we determine if n can be expressed as the sum of the squares of two whole numbers?

e). The number 25 can be expressed as the sum of two perfect squares in two ways:
25 = 0²+5² = 3²+4².
Find another number that can be expressed as the sum of two perfect squares in two ways.

f). Find one number that can be expressed as the sum of two perfect squares in three ways.

g). What is the maximum number of ways a number can be expressed as the sum of two perfect squares?

h). Share your own problem inspired by this one.

i). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.