Arithmetic Progressions and Binary Quadratic Forms
نویسندگان
چکیده
is a (nonconstant) arithmetic progression of positive integers. We consider a general binary quadratic form ax2 + bxy + cy' ( a , b , c E Z ) and ask the question "Can the form ax' + hxy + ry' represen1 every inleger in 1he arithmetic progression kNo + 1 for any natural numbers k and l?" In a sampling of books containing a discussion of binary quadratic forms [2]-[9], we did not find this qustlon treated. In answering our question we shall see that the discriminant d = b' 4ac E Z of the form ax' + bxy + cy2 plays a key role. We prove:
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 115 شماره
صفحات -
تاریخ انتشار 2008