Possible idea:

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Define r=1/c

Define sum[1/i] i:2->n = sumH(n)

If k*r for any integer k>1 equals any 1/i then k and i are solutions

Choose starting point x such that 1<x<c

Choose a range over which to search e.g. 100 consecutive numbers

Calculate starting remainder r(x)=x/c

Calculate sum of remainders for c, S_r=r(x)+(100-1)*r

Calculate sum of harmonic series for same range S_h=sumH(x+100)-sumH(x)

Evaluate S_r,S_h

If all 100 consecutive numbers are factors of c then S_r-S_h=0

Where I am stuck is what if none of 100 numbers are factors?

What is some relation with S_r,S_h in that case? We know c.

If we figure this out we can construct a log(n) algorithm. Half the search space when match found.

Shitposting because I am bored.

Ignore similarities in variables names to those related to The Grid.

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a

b

f=atan(a/b)

d=sqrt(a^2+b^2)

c=ab

c=d^2sin(f)cos(f)

c=(a/b)*(a^2+b^2)/(a^2/b^2+1)

An interesting thing emerges:

ab=(a/b)*(a^2+b^2)/(a^2/b^2+1)

If we could define a,b such that a^2+b^2=a^2/b^2+1 then ab=a/b

When we try to solve this in complex we get:

a=b*sqrt((1-b^2)/(b^2-1))

a=b*i

Multiplying by i is just mirroring a point over 45deg angle?