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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soln

| Comment 1 of 5

computer, brute force:

2 2 3 6 6 (also - no solutions found for 4 fractions)

program cub

implicit none

integer i1,i2,i3,i4,i5,itol,itop,itell

real x1,x2,x3,x4,x5,a2,a3,a4,sum,tt,err

itell=10

tt=2./3.

itop=200

itol=6

err=10.**(-itol)

do 1 i1=2,itop

if((i1/itell)*itell.eq.i1)print*,i1, 'out of ',itop

x1=1./i1**2

do 2 i2=2,itop

x2=1./i2**2

a2=x1+x2

if(a2.gt.tt) go to 2

do 3 i3=2,itop

x3=1./i3**2

a3=a2+x3

if(a3.gt.tt)go to 3

do 4 i4=1,itop

x4=1./i4**2

a4=a3+x4

if(a4.gt.tt)go to 4

do 5 i5=2,itop

x5=1./i5**2

sum=a4+x5

if(sum.gt.tt)go to 5

if(abs(sum-tt).lt.err)then

print*,i1,i2,i3,i4,i5

stop

endif

5 enddo

4 enddo

3 enddo

2 enddo

1 enddo

end

Edited on August 25, 2020, 10:05 am

Posted by Steven Lord on 2020-08-25 09:56:07

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