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PERFECT NUMBERS: AN ELEMENTARY …
WebIntersection number. In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency. One needs a definition of intersection number in order to state ... WebTHEOREM 1. If k > 1, then I(kN) > I(N). Proof. If 1, a,, a2,..., at, N are the divisors of N, then 1, k, kal, ka2,..., kat, kN is a (perhaps incomplete) list of divisors of kN. Thus, I(kN) >(1+k+ka1+ka2+ +kN)/kN =1/kN+ (1 + a, + a2 + +N)/N =1/kN+I(N) >I(N). This theorem captures the 13th century assertions that every multiple of a perfect number is marty magee\u0027s irish pub pa
Divisors of 27 - Mathstoon
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