1. Find a triple {a, b, c} of three distinct natural numbers (without zero) a, b and c with the following property:
a+b, a+c, b+c, ab, ac, bc are all perfect squares.
2. Find an efficient method to generate all triples with the above property.
3. Find a quadruple, quintuple with the above property.
Set of natural numbers
Re: Set of natural numbers
So you want someone to just hand you the answer to problem 142, do you?

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Re: Set of natural numbers
Hint:
2^{i}3^{j}, 2^{k}3^{ℓ} and 2^{m}3^{n} is 2^{max(i,k,m)}3^{max(j,ℓ,n)}.
2^{i}3^{j}, 2^{k}3^{ℓ} and 2^{m}3^{n} is 2^{max(i,k,m)}3^{max(j,ℓ,n)}.
WHUK