Unformatted text preview: x and y satisfying x 2 + y 2 = n. 5. Give an example of a positive integer n such that 9  n and such that there are integers x and y with the property that x 2 + y 2 = n. (Give an example of such an x and y .) 6(a). Suppose m is a positive integer with the property that there are no positive integers x and y satisfying x 2 + y 2 = m. Prove that there cannot be any positive integers x and y satisfying x 2 + y 2 = 9 m. 6(b). Give an example of a number k such that 9  k and yet there are no integers x and y with the property that x 2 + y 2 = k . 7(a). Prove (any way you like) that there are no integers x,y,z satisfying x 2 + y 2 + z 2 = 7 . 7(b). Prove that if m has the property that there are no integer solutions to x 2 + y 2 + z 2 = m, then there are also no integer solutions to x 2 + y 2 + z 2 = 4 m. Give a formula that describes an inﬁnite set of integers that cannot be written as a sum of three integer squares....
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 Fall '07
 COURTNEY
 Math, Natural number, positive integer, 4m

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