Re: Interesting property problem

On Sep 30, 7:15 pm, Saysero <says...@xxxxxxxxx> wrote:
Let n in N and a_i for 1<=i<=n in N and a_1<a_2<...<a_n. If for every
1<=i<j<n number (a_j + a_i) is divisible by (a_j - a_i) then the
finite sequence a_1,...,a_n has the property $.
Problem: Show that for every n>=2 there is a finite sequence
a_1,...,a_n that has the property $.
Can anyone please help me solve this?
Thanks in advance.

P.S.
I tried induction. My idea was to construct a_{n+1} if a_1,...,1_n
have the property $ so that a_1,...,a_{n+1} still has the same
property. This is however impossible since a_1=1, a_2=2 and a_3=3 have
the property $ but no x can be found such that x+1 is divisible by x-1.

Is there anyone who can help me solve this problem?
.

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