sample3 - 6. Determine whether or not 2 3 3 2 11 5 can be...

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Math 465, Sample Exam III SHOW ALL WORK. INDICATE ALL REASONING. 1. Go over all the problems on the midterms, sample exams, and homework. 2. Find all integer solutions to the linear Diophantine equation 252 x + 66 y = 6000 . 3. Find all primitive Pythagorean triples { x, y, z } containing 17. 4. If { x, y, z } is a Pythagorean triple, prove that 3 | xy . 5. Determine whether or not the Diophantine equation x 2 + y 2 = 3 z 2 has nontrivial solutions.
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Unformatted text preview: 6. Determine whether or not 2 3 3 2 11 5 can be expressed as the sum of two squares. (Justify your answer.) 7. Determine whether or not 3 3 17 can be expressed as the sum of three squares. (Justify your answer.) 8. Prove that if n is composite, then n can be written in the form n = x 2-y 2 , with y + 1 < x . 9. Determine whether or not 8128 is a perfect number. 1...
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