9. The famous Waring problem (formulated in 1770) was to show that every positive integer can...

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9. The famous Waring problem (formulated in 1770) was to show that every positive integer can be written as the sum of at most four perfect squares. David Hilbert was the mathematician who finally solved this problem in 1909. So, for example, 11 = 32 + 1? + 12+ 12 and 87 = 22 + 3? + 52 + 7? and 31 = 5 + 2° + 12 +12. Find the Waring/Hilbert decomposition of 101. Find the Waring/Hilbert decomposition of 1001. Write a computer program that will perform this job for you. Discuss this problem in class. 9. The famous Waring problem (formulated in 1770) was to show that every positive integer can be written as the sum of at most four perfect squares. David Hilbert was the mathematician who finally solved this problem in 1909. So, for example, 11 = 32 + 1? + 12+ 12 and 87 = 22 + 3? + 52 + 7? and 31 = 5 + 2° + 12 +12. Find the Waring/Hilbert decomposition of 101. Find the Waring/Hilbert decomposition of 1001. Write a computer program that will perform this job for you. Discuss this problem in class.