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Royalty
guest
Jun-02-03, 08:41 AM (EST)

"Egyptian Fractions"

 This is a very hard problem to solve.The term Egyptian fractions refers to those fractions whose numerator is 1 and whose denominator is any other whole number.How can the fraction 19/94 be expressed as the sum of two Egyptian fractions?

alexb
Charter Member
978 posts
Jun-02-03, 08:58 AM (EST)

1. "RE: Egyptian Fractions"
In response to message #0

>This is a very hard problem to solve.

On the contrary, it's very easy to solve.

>The term Egyptian fractions refers to those fractions whose
>numerator is 1 and whose denominator is any other whole
>number.

>How can the fraction 19/94 be expressed as the sum of two
>Egyptian fractions?

Has this problem come out of the blue? Have you ever solved similar problems?

There's what's known as the greedy algorithm.

### Basic step:

Subtract from a given fraction the largest Egyptian fraction that leaves a positive difference.

### Recursive step:

If the difference is an Egyptian fraction, stop. Otherwise, apply the Basic step to the difference.

For the difficult case of 19/94 it takes exactly one basic step.