Find all positive integer triples , with and squarefree and

Then .

Since ,

we must have and , so and .

Hence , like , is squarefree, and so are and

since their product is squarefree

Thus we have the necessary conditions:

are all squarefree; ,

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There are an infinite number of triples where :-

a = b = 2^(n+1) – 2 and

c = 4^(n+1) – 2^(n+3) + 3

For all n, here are the first 10, format {a, b, c}.

{2,2,3}

{6,6,35}

{14,14,195}

{30,30,899}

{62,62,3843}

{126,126,15875}

{254,254,64515}

{510,510,260099}

{1022,1022,1044483}

{2046,2046,4186115}

Paul.

I get different results

yes some are the same, seems you get some I don’t and I get some you don’t.