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Joined: 07 May 2014
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How many pairs have one or more prime factors common
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Updated on: 13 May 2014, 01:04
Question Stats:
79% (00:40) correct 21% (00:54) wrong based on 110 sessions
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How many pairs (n, n+1) have one or more prime factors common, where n is an integer and 2 ≤ n ≤9 ? A. 0 B. 1 C. 2 D. 3 E. 4 Can someone have a go at this question and explain how to work this problem. The explanation simply states that this is a generalization of an elementary theorem in number theory.
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Originally posted by dxx on 12 May 2014, 14:02.
Last edited by Bunuel on 13 May 2014, 01:04, edited 1 time in total.
Edited the question.



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Re: How many pairs have one or more prime factors common
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12 May 2014, 14:15
Prime numbers between 2 and 9: 2, 3, 5, 7. Each of this number isn't a factor of him+1, as simple as that.



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Re: How many pairs have one or more prime factors common
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12 May 2014, 19:19
Quickly look at the pairs (2,3)  nothing common (3,4)  nothing common (4,5)  nothing common (5,6)  nothing common (6,7)  nothing common (7,8)  nothing common (8,9)  nothing common (9,10)  nothing common Hence A
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Re: How many pairs have one or more prime factors common
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13 May 2014, 01:06



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Re: How many pairs have one or more prime factors common
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13 May 2014, 12:58
Solved this fairly easily by writing out the primes for 2 thru 9, and noticed no consecutive integers shared any prime factors...
2  2 3  3 4  2,2 5  5 6  2,3 7  7 8  2,2,2 9  3,3



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Re: How many pairs have one or more prime factors common
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11 Aug 2017, 10:03
consecutive numbers have no prime factors in common



Intern
Joined: 04 Aug 2017
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How many pairs have one or more prime factors common
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12 Aug 2017, 00:05
Rule is that consecutive integers will not have common factors except 1 (and 1 is not a prime number).




How many pairs have one or more prime factors common &nbs
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12 Aug 2017, 00:05






