PROBLEMSAND SOTUTIONS
EDITORS
Curtis Cooper
CMJProblems
Departmentof Mathematicsand ComputerScience
Universityof CentralMissouri
Wanensburg,MO 64093
email: cooper@ucmo.edu
Shing S. So
CW Solutions
Depaftmentof Mathematicsand ComputerScience
Universityof CentralMissouri
MO 4093
Warrensburg,
email:so@ucmo.edu
We urge
Thissectioncontainsproblemsthatchallengestudentsandteachersof collegemathematics.
youto participateactivelyby submittingsolutionsand by proposingproblemsthat are newand interthatspanthe entireundergraduate
esting.To promotevariety,the editorswelcomeproblemproposals
curriculum.
Proposedproblemsshouldbe sent to Curtls Cooper,eitherby emailas a pdf' T5[' or Word
possible,a proposedprob(preferred)
or by mailto theaddressprovidedabove.Whenever
attachment
any
othermaterialthat would
and
references,
by a solution,appropriate
lem shouldbe accompanied
shouldsubmitproblemsonlyif the proposedproblemis not under
be helpfulto the editors.Proposers
by anotheriournal.
consideration
Solutionsto the problemsin this issue shouldbe sentto Shing So, eitherby emailas a pdf'
(prefened)or by mailto theaddressprovidedaboveby April15,2009.
Tg[, or Wordattachment
PROBLEMS
891.proposed by william P wardlaw, u. s. Naval Academy,Annapolis, Maryland..
LetV bean n dimensionalvector spaceover the q elementfinite field Fn. Showthat the
r nonzerovectorsin V can be listed in orderTr,62, . . . ,T, suchthat for any positive
integerft, @*,T*+t, . . . ,6n+o-r) (interpretingsubscriptsmodulo r) is an orderedbasis
for V.
892. Proposedby Greg Omnn, The Ohio State University, Columbus,Ohio.
Find all rings R (not assumedto be commutative of to contain an identity) with the
following two properties:
(i) not every element of R is nilpotent, and
(ii) x2 y2 for any nonzerox, y e R.
893. Proposedby Ovidiu Furdui, University of Toled'o,Toledo,Ohio.
Let f be any function that has a Taylor seriesrepresentationat 0 with radius of convergence1, and let
f'(0)
T ,(x\:f( 0) + ?ix+ ...+
f(')(0) -
JOURNAL
VOL.40, NO. T,JANUARY2OO9THE COLLEGEMATHEMATICS
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