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[VA] SRC #008 - 2021 is here !
01-05-2021, 07:42 PM (This post was last modified: 01-05-2021 11:45 PM by Albert Chan.)
Post: #22
RE: [VA] SRC #008 - 2021 is here !
(01-05-2021 06:32 PM)Valentin Albillo Wrote:  
  • It is trivially easy to express the fraction 4/2021 as the sum of 4 numbers of the form 1/N where N is a positive integer, namely:

                4/2021   =   1/2021 + 1/2021 + 1/2021 + 1/2021

    See if you can do it with just 3 such numbers.

Code:










2021 = 43 * 47

1/(43*k1) + 1/(47*k2) + 1/(2021*k3) = 4/2021

47/k1 + 43/k2 + 1/k3 = 4

if k = k1 = k2, we have 90/k + 1/k3 = 4

k3 = 1/(4-90/k) = k/(4*k-90) = integer

k=24 → k3=4    → 4/2021 = 1/1032 + 1/1128 + 1/8084
k=30 → k3=1    → 4/2021 = 1/1290 + 1/1410 + 1/2021

Of course, there are many more solutions, if k1 ≠ k2
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Messages In This Thread
RE: [VA] SRC #008 - 2021 is here ! - Gene - 01-02-2021, 01:49 AM
RE: [VA] SRC #008 - 2021 is here ! - robve - 01-03-2021, 06:33 PM
RE: [VA] SRC #008 - 2021 is here ! - robve - 01-05-2021, 03:39 AM
RE: [VA] SRC #008 - 2021 is here ! - Gene - 01-04-2021, 05:56 PM
RE: [VA] SRC #008 - 2021 is here ! - Gene - 01-04-2021, 07:24 PM
RE: [VA] SRC #008 - 2021 is here ! - Albert Chan - 01-05-2021 07:42 PM
RE: [VA] SRC #008 - 2021 is here ! - Gene - 01-06-2021, 02:54 PM
RE: [VA] SRC #008 - 2021 is here ! - EdS2 - 01-08-2021, 01:32 PM



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