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.
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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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