Find all positive integers $n$ such that the set
${n,n+1,n+2,n+3,n+4,n+5}$
can be split into to disjoint subsets such that the products of elements in these subsets are the same.
[This probolem can be solved without using any theorem! ]
IMO 1970
 Kazi_Zareer
 Posts: 86
 Joined: Thu Aug 20, 2015 7:11 pm
 Location: Malibagh,Dhaka1217
Re: IMO 1970
Try yourself
We cannot solve our problems with the same thinking we used when we create them.

 Posts: 11
 Joined: Tue Jun 16, 2015 5:11 am
 Location: Barisal, Bangladesh
Re: IMO 1970
By contradiction we assume that there exist a n such that that satisfy this proposition. there is a number in those there must be a number which is divisible by 5. so that , we have another number which is divisible by 5. suppose those number are n , n+5 . now n+1, n+2, n+3, n+4 none of them will not be divisible by any p>5 because we can't have two such prime divisor into another's. two of them must be even. so that they must be power of 3 . two consecutive even number can't be power of 3 unless they are 1,3 . so we have such a answer n=0. but this is not positive integer. so that there does not exist such an integer n that satisfy the proposition