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The First Skewed Contest!
Math Contest #1
Number of Divisors
The
study of number theory reveals many of the fundamentals of our number
system. It is of considerable interest that much of the current research
in computers and algorithmic methods have solutions rooted in the essence
of numbers and their properties. In an effort to reward and excite people
in their pursuit of often overlooked subjects, Skewed Perspective is sponsoring
the first in a series of ongoing math contests.
This
contest is designed for people with an interest in pure or applied mathematics.
It is an open-ended contest that will conclude with the receipt of the
first correct answers. It may require the use of programming which can
be accomplished on math software or on any computer science department’s
system. However, the level of difficulty does not excede the material
taught in a first semester of programming nor does it excede a general
familiarity with mathematical methods of proof or algorithms.
Background
d(n)
is defined as the number of positive divisors of the integer n (including
1 and n)
Some
examples are:
d(6)
= 4
divisors
{ 1 , 2 , 3 , 6 }
d{12}
= 6
divisors { 1 , 2 , 3 , 4 , 6 , 12 }
d(27)
= 4
divisors { 1 , 3 , 9 , 27 }
This contest is interested in finding consecutive groups of integers with
the same d(n). One of the first groups of three is the set { 33
, 34 , 35 } .
d(33) = d(34) = d(35) = 4
33 has divisors { 1 , 3 , 11 , 33 }
34 has divisors { 1 , 2 , 17 , 34 }
35 has divisors { 1 , 5 , 7 , 35 }
The contest is split into two parts.
Can you find the first group of ten consecutive integers with equivalent
d(n)?
Can you find the first group of fifteen consecutive integers with equivalent
d(n)?
The possibility that some parts of this study of integers have already
been examined is strong. Therefore, successful completion of this contest
will require the submission of:
-the consecutive set of integers
-a list of their respective divisors
-a brief synopsis of your methods in findng the solution
-a copy of the mathematical computations that yielded your results
or
-a copy of the source code of your program with some documentation of
unclear sections
To assist your quest, the next set of three consecutive integers is {
85 , 86 , 87 } and the first set of four consecutive integers is { 242
, 243 , 244 , 245 }.
The prize:
$50.00
($25.00 for the first set of ten consecutive integers, $25.00 for the
set of fifteen consecutive integers)
This contest is intended for undergrad students... Please contact Brad
Abbott at: babbott@skewedperspective.com to enter and for any questions...
Good luck!
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