Vol. 10 No 3 - Pi Mu Epsilon

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PI MU EPSILONVOLUME 10 FALL 1995 NUMBER 3CONTENTSA correspondence on telescoping seriesDan Kalman and John Mathews 169..................A weighted AM-GM-HM inequalityAyoub B. Ayoub ............................................ 183On the girths of regular planar graphsMasakazu Nihei ............................................. looPrediction in insuranceMark Bonsall ................................................. 191An application of partitions to the factorizationof polynomials over finite fieldsJulia Varbalow and David C. Vella 194.............A characterization of quadratfrei LucaspesudoprimesPaul S. Bruckman ......................................... 207Enumerating partitionsRachele Dembowski......................................(continued on inside back cover)i ,:,;,ej^'^ 6 lu- ,,212 ^,,?-- ^-Si-r
THE OFFICIAL PUBLICATION OF THEEditor: Underwood DudleyProblems Editor: Clayton W. DodgeOfficers of the SocietyPresident: Robert C. Eslinger, Hendrix CollegePresident-Elect: Richard L. Poss, St. Norbert CollegeSecretary-Treasurer: Robert M. Woodside, East Carolina UniversityPast-President: David W. Ballew, Northern Illinois UniversityCouncilorsJ. Douglas Faires, Youngstown State UniversityDoris Schattschneider, Moravian CollegeBrigitte Servatius, Worcester Polytechnic InstituteRobert S. Smith, Miami UniversityEditorial correspondence, including manuscripts, chapter reports, andnews items should be sent to Underwood Dudley, Mathematics Department,DePauw University, Greencastle, Indiana 46135 (e-mail addressdudley@depauw.edu). Students submitting manuscripts should give theirschool and date of graduation. Others should provide their affiliation,academic or otherwise.Problems for solution and solutions to problems should be sent directlyto Clayton W. Dodge, Mathematics Department, 5752 Neville Hall,University of Maine, Orono, Maine 04469.The Pi Mu EPSILON JOURNAL is published at DePauw University twicea year-Fall and Spring. One volume consists of five years (ten issues)heginning with the Fall l9n9 or Fall 19(n + 1)4 issue, n - 4, 5, . . . , 8.Dear Dan,November 23It was good to see you at the MAA Section meeting last weekend. 1meant to tell you about a problem 1 have been working on, which I thinkmight interest you. I got interested in it one day while fooling around withMatheniatica. I think that programs like Matheniatica offer realopportunities for students to make their own niatheniatical discoveries, andwas working on one possible direction for exploration-telescoping series.You know the standard example?and all the terms cancel except the first so the sum is I. I was looking forgeneralizations. One obvious sum to consider isProceeding as in the first example, I used a partial fractions decompositiontor the sumnian~l. Mathematica has a built-in function for this, you kno\v,so it is really effortless to see what will happen. Anyway, here is whatcame out:As before, the sum telescopes. To simplify the notation. niiiltiply both sick's
Page 4 and 5: KALMAN AND MATHEWS. TELESCOPING SER
Page 6 and 7: KALMAN AND MATHEWS, TELESCOPING SER
Page 8 and 9: KALMAN AND MATHEWS, TELESCOPING SER
Page 10 and 11: A WEIGHTED AM-GM-HM INEQUALITYDan K
Page 12 and 13: ON THE GIRTHS OF REGULAR PLANAR GRA
Page 14 and 15: Acknowledgment: The author would li
Page 16 and 17: VARBALOW AND VELLA, FACTORIZATION O
Page 18 and 19: VARBALOW AND VELLA, FACTORIZATION O
Page 20: VARBALOW AND VELLA, FACTORIZATION O
Page 23 and 24: CONJECTURE 3: z(p2) = pZ(p) for all
Page 25 and 26: Rachele DernbowskiSUNY, Stony Brook
Page 27 and 28: SEME, HASSE SUBGROUP DIAGRAMS 217wh
Page 29: pylp? ...p~...p? ...p? > - A.Applyi
Page 33 and 34: PROBLEMS AND SOLUTIONS 229married c
Page 35 and 36: PROBLEMS AND SOLUTIONS836. [Fall 19
Page 37 and 38: PROBLEMS AND SOLUTIONS91, 92, a tot
Page 39 and 40: PROBLEMS AND SOLUTIONS 24 1then xy'
Page 41 and 42: that:a) Triangles ABC. PQR,and W7.
Page 43 and 44: 248 Pi MU EPSILON JOURNALso that x
Page 45 and 46: 252 PI Mu EPSILON JOURNALcertain. A
Page 47: Subscription and Change of AddressI

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