The Five Powers

Powers from five terms in arithmetic progression

has only the solution (n, k, b, y, l) = (48, 3, 6, 140, 2) in positive integers n, k, b, y and l, where k, l ≥ 2, P (b) ≤ k and P (y) > k. Here, P (m) denotes the greatest prime factor of the integer m (where, for completeness, we write P (±1) = 1 and P (0) = ∞). Rather surprisingly, no similar conclusion is available for the frequently studied generalization of this equation to products of con...

Symmetric powers and the Satake transform

‎This paper gives several examples of the basic functions‎ ‎introduced in recent years by Ng^o‎. ‎These are mainly‎ ‎conjectures based on computer experiment‎.  

Government’s Powers and FTAs: The Effect of Domestic and Foreign Powers on Multilateral Trade

This paper elaborates on the government's powers - both at the domestic level and over foreign countries. The domestic power is the power against domestic lobbies, and the foreign one is the government's international power. To do so, this paper tries to evaluate the effects of these powers   on the formation of free trade agreements (FTAs). The theoretical framework follows an oligopolistic-po...

Proposal Powers, Veto Powers, and the Design of Political Institutions

Comparing Powers and Symbolic Powers of Ideals

We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...