All about problems in Volume 115. If there is a thread about your problem, please use it. If not, create one with its number in the subject.
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You may apply this lemma in your approach:
You may also read this to improve the performance of your solution.
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Suppose that n and d are relatively prime positive integers. Then n/d is the sum of two unit fractions if and only if there are positive integer divisors A and B of d such that A+B is divisible by n.
I apparently found a very quick way to find x y and z with even numbers and odd numbers in the form 3 + 4k, all based on the 4/n thing that you can write it as a form of 2 unit fractions. But I would like to know how to calculate for prime numbers !