A 9

[Peter]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#1

A 9

[Ilthigore]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#2

Clearly the only common prime factors amongst 10 consecutive positive integers will be 2,3,5,7.

5 of them will be divisible by 2, at least one of which must also be divisible by 3 and at least one of which must also be divisible by 5, and, if two of the numbers are divisible by 7, one of them will be even.

This leaves two multiples of 3, one multiple of 5, and one multiple of 7 unaccounted for, enough factors to dish out to 4 more of our integers.

But this still leaves one integer not divisible by 2,3,5,7, and therefore co-prime with all other integers of the set, and so coprime with their product.

[manjil]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#3

Generalisation?

[Peter]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#4

Can you post your example for 25? Maybe that gives us a clue.

[MayankM]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#5

I have read some where that this result is true for n up to 16 consecutive integers. I'll look up the source and post soon.

[manjil]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#6

Re:Generalisation

[Peter]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#7

Re:Generalisation

[Jure the frEEEk]

Not_yet_rated Poor (Spam) Poor (Spam) Below average Below average Average Average Good Good Very good Very good Excellent

To rate posts you must be logged in

#8