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For n >= 1, 4/n = 1/a + 1/b + 1/c, has postive integer solutions.

n = 2k (evens)

n = 4k+3 (odds)

n = 4k+1 (odds)

For 2k I have found the pattern --> if k >= 1, 4/2k = 1/2k + 1/2k + 1/k. This is simple, I know.

I am having difficulty finding the pattern for 4k+3 (no pattern has yet been found for 4k+1, I know).

So what is the pattern for:

4/4k+3 = 1/a + 1/b + 1/c

?

Does anyone know this pattern? If you do, please reply with such pattern.

Thank you

J.E.H.