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Question Number 46751 by Joel578 last updated on 31/Oct/18
Prove that there exist 4 distinct positive integers  such that each integer divides the sum of the   remaining integers.
$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{4}\:\mathrm{distinct}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{each}\:\mathrm{integer}\:\mathrm{divides}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{remaining}\:\mathrm{integers}.\: \\ $$
Commented by MrW3 last updated on 31/Oct/18
n,2n,3n,6n with n∈N
$${n},\mathrm{2}{n},\mathrm{3}{n},\mathrm{6}{n}\:{with}\:{n}\in\mathbb{N} \\ $$
Commented by Joel578 last updated on 31/Oct/18
please explain how to get those numbers, Sir
$$\mathrm{please}\:\mathrm{explain}\:\mathrm{how}\:\mathrm{to}\:\mathrm{get}\:\mathrm{those}\:\mathrm{numbers},\:\mathrm{Sir} \\ $$
Commented by MrW3 last updated on 31/Oct/18
try and see.  I think there exist many other numbers which  also fulfill the condiction, e.g.  n,4n,5n,10n.
$${try}\:{and}\:{see}. \\ $$$${I}\:{think}\:{there}\:{exist}\:{many}\:{other}\:{numbers}\:{which} \\ $$$${also}\:{fulfill}\:{the}\:{condiction},\:{e}.{g}. \\ $$$${n},\mathrm{4}{n},\mathrm{5}{n},\mathrm{10}{n}. \\ $$

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