what are the 3 integers in arithmetic seq. w/ prime product?  TOPIC_SOLVED

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what are the 3 integers in arithmetic seq. w/ prime product?

Postby marty.frmn on Sun Nov 01, 2009 9:57 pm

what are the 3 integers in arithmetic sequence whose product is prime????
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Postby stapel_eliz on Mon Nov 02, 2009 11:19 am

Since primality is a property of whole numbers, and since 1 and 0 are not primes, then 0 cannot be one of the numbers. Also, the product must be positive and greater than 1. In addition, you cannot have an even number in the sequence, since then 2 would be a factor, and the product would not be prime.

If the three integers (call them r, s, and t) are non-trivial, then their product, rst, will generally be non-trivial. Clearly none of them can be zero or even. The only factors which can safely be ignored are 1 and -1, as they "collapse" into the product.

Can you think of a way to work with these two values, and possibly one or two others, to create an arithmetical sequence (a string of three equidistant values) whose product rst > 1 is prime? :wink:
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Re: what are the 3 integers in arithmetic seq. w/ prime product?  TOPIC_SOLVED

Postby marty.frmn on Mon Nov 02, 2009 7:48 pm

yep.... got that one....
with -1 and 1.... comes along -3 which is neither an even number nor a 0....
so they satisfy the product being a prime condition and are in arithmetic sequence....
so the numbers have to be -3,-1 and 1.... :)
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Postby stapel_eliz on Mon Nov 02, 2009 8:20 pm

That's what I came up with, too. Good work! :wink:
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