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21 May 2005: 24) Show that the repetition code of length n is perfect if and only if n is odd.

10 Nov 2005: 24) Show that an Eulerian plane map is 2-colourable. 25) Let S be the projective plane.

14 Mar 2005: Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs. W. T. Gowers. Abstract. The main results of this paper are regularity and counting lemmas for 3-. uniform hypergraphs. A combination of these two results gives a new proof of a

12 Apr 2005: Hypergraph Regularity and the multidimensional Szemerédi Theorem. W. T. Gowers. Abstract. We prove analogues for hypergraphs of Szemerédi’s regularity lemma and the. associated counting lemma for graphs. As an application, we give the first

24 Nov 2005: T.A.Fisher@dpmms.cam.ac.uk - 1 - 24 November 2005. 54) Alice and Bob are issued with RSA public keys (N, e1) and (N, e2), and correspondingprivate keys (N, d1) ... Show that the sequence in (ii) has period 2d 1. T.A.Fisher@dpmms.cam.ac.uk - 2 - 24