perplexus.info :: Just Math : Square Reciprocal Summation

Square Reciprocal Summation (Posted on 2020-08-25)

{3,3,3,3,3,3} is a set of six integers such that the sum of the squares of the reciprocals totals 2/3.
(1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 = 2/3

Does there exist a set of integers with fewer than 6 members whose sum of the squares of the reciprocals totals 2/3?

Problem inspired by Find the triplets

No Solution Yet Submitted by Brian Smith

Rating: 3.0000 (1 votes)

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UBASIC solution

| Comment 2 of 5 |

(In reply to soln by Steven Lord)

10 dim d(6)

20 gosub *addon(1)

30 end

40 *addon(wh)

50 local i,j

60 if wh=1 then st=2: else st=d(wh-1)

70 i=st

80 repeat

90 tot=tot+1//(i*i)

100 d(wh)=i

110

120 if tot=2//3 then

130 :for j=1 to wh:print " ";d(j);:next:print

140 :else

150 :if wh<6 and tot<2//3 then gosub *addon(wh+1)

160

170 tot=tot-1//(i*i)

180 i=i+1

190 until (6-wh)//(i*i) < 2//3 - tot

200 return

finds that using the squares the reciprocals of 2, 2, 3, 6 and 6 leads to a total of 2/3.

Posted by Charlie on 2020-08-25 11:22:20

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