Unformatted text preview: 70 and 70, and verify that the primes that occur are precisely the ones predicted by your answer in part (a). 5. Using quadratic reciprocity as in part (a) of the previous problem, Fgure out which primes are represented by at least one form of discriminant for the following values of :3, 8,20, 21. 6. (a) Repeat the previous problem for = 9 where the answer may be rather surprising. Note that quadratic forms with = 9 are 0hyperbolic, rather than the more usual hyperbolic or elliptic forms that we consider. (0hyperbolic forms factor into linear factors with integer coecients.) (b) Draw enough of the topographs of all three equivalence classes of forms with = 9 to see why the answer you got in part (a) is correct. (c) Show that in fact every integer n is represented primitively by at least one quadratic form of discriminant 9....
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 Fall '07
 LOZANOROBLEDO
 Math, Number Theory, Prime number, previous problem, hyperbolic forms factor

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