Brainsteem Mathematics Challenges - Sums of Squares 2017

A) If we wish to write the number 2017 as the sum of k distinct square numbers, what is the minimum value of k?

B) If we wish to write the number 2017 as the sum of q squares of prime numbers, not necessarily distinct, what is the minimum value of q?

For example, 26 = 1² + 5², so k=2, but if we restrict ourselves to prime number squares, then 26 = 2² + 2² + 3² + 3², so that q=4.

Have fun!

As always, these questions are adapted from one of the many mathematics competitions around the world, and are designed to be done by hand, without even a calculator! Those questions that are on computational mathematics will be entitled "Brainsteem Compute".

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There has been a long gap since my last post on mathematics. I have been managing the Minnows Accelerator Project (MAP) and that has taken most of my time. But I shall also now return to posting on subjects that interest me!

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