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Re: An Algebra 2 Test
Posted:
Dec 4, 2012 12:03 PM
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On Dec 3, 2012, at 2:36 PM, Dave L. Renfro <renfr1dl@cmich.edu> wrote:
> Carl Pomerance, "A tale of two sieves", Notices of the American
> Mathematical Society 43 #12 (December 1996), 1473-1485.
> http://www.ams.org/notices/199612/pomerance.pdf
"I was involved in a math contest, and one of the problems was to factor the number 8051. A time limit of five minutes was given. It is not that we were not allowed to use pocket calculators; they did not exist in 1960, around when this event occurred! Well, I was fairly good at arithmetic, and I was sure I could trial divide up to the square root of 8051 (about 90) in the time allowed."
5 minutes is a lot of time. Like the author (thought), if I didn't immediately know any better I would have solved this the less sophisticated way. To get a "1" at the end, a pair of factors must end in 1 and 1, 3 and 7 or 9 and 9. It didn't take long on my drive home to get to 97 x 83. Of course, it would have more time, but doable in 5 minutes, if the factors had been far apart.
This whole paper would be a very cool project for a high school junior or senior.
Bob Hansen
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