Number of ways a integer can be written as sum of fractions
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I will produce a method to use for counting. Let
1n=1a+1b1n1a1b.
Then
ab=na+nbabnanb
and so
(a−n)(b−n)=n2anbnn2
Further let pp and qq be two integers which multiply to n2n2.
Then, there is a solution for each value of nn since a=p+napn.
HOWEVER, since you need something to do, this method counts some solutions twice. So answer the following:
If nn can be written as the product of two positive integers in kk ways, in how many ways can 1n1n be written as the sum of two unit fractions?
1n=1a+1b1n1a1b.
Then
ab=na+nbabnanb
and so
(a−n)(b−n)=n2anbnn2
Further let pp and qq be two integers which multiply to n2n2.
Then, there is a solution for each value of nn since a=p+napn.
HOWEVER, since you need something to do, this method counts some solutions twice. So answer the following:
If nn can be written as the product of two positive integers in kk ways, in how many ways can 1n1n be written as the sum of two unit fractions?
Answered by
0
There are infinite no. of ways
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