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Primary Product (Posted on 2003-06-02) Difficulty: 2 of 5
Do there exist three integers in Arithmetic Progression whose product is prime ? If Yes, then what are the three integers and if No, then why ?

[Note: The numbers: x1, x2, x3, x4, x5, x6,........ are said to be in Arithmetic Progression if (x2 - x1) = (x3 - x2) = (x4 - x3) = (x5 - x4) = ........ and so on].

See The Solution Submitted by Ravi Raja    
Rating: 2.7778 (9 votes)

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re(3): Umm | Comment 7 of 25 |
(In reply to re(2): Umm by Gamer)

3 X 5 X 7 is by definition composite, as its factors are not just itself(105) and 1, but rather have 3, 5, 7, 15, 35 and 21 as factors also.

With two negatives and two integers that have absolute value 1, the answer given is the only one. The factors can only be (in absolute value) the prime number itself and one. Any arithmetic progression that has numbers all larger than 3 must necessarily produce composite numbers, not primes.
  Posted by Charlie on 2003-06-02 09:30:37

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