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Quadratic systems of circles in non-euclidean geometry

1919
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Bulletin of the American Mathematical Society
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1919.] QUADRATIC SYSTEMS OF CIRCLES. 161 For an even X, this becomes a -OL<L + #4 -• • • = 1. For any X, there is a\ -a 3 + OJ 6 -• • • = 0. When X is odd, then -a + OL% -a\ + • • • = 1. When n is odd, say n = 2X + 1, then a -«2 + «4 ~ • • • = 0, and a% -az + «5 -• • • = 1, when X is odd; -ai + a 3 -as + • • • = 1, when X is even. We shall, in particular, consider the case where (15) has the form (16) in which n and A must both be either even or odd in order that (16) may reduce to (14) for u =

doi:10.1090/s0002-9904-1919-03171-1
fatcat:5bpwwsa3fvepzdadgd2wbabyay