Set of natural numbers

Primes, divisors, arithmetic, number properties, ...
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ThrowawayUsername
Posts: 1
Joined: Thu Sep 24, 2015 12:51 pm

Set of natural numbers

Post by ThrowawayUsername » Thu Sep 24, 2015 1:00 pm

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, a-b, a-c, b-c 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.

whatteaux
Posts: 5
Joined: Mon Sep 24, 2012 10:58 am

Re: Set of natural numbers

Post by whatteaux » Fri Sep 25, 2015 12:29 am

So you want someone to just hand you the answer to problem 142, do you?

KelSmi68
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Joined: Sat Oct 10, 2015 10:22 am
Location: Morley, Leeds, West Yorkshire, UK
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Re: Set of natural numbers

Post by KelSmi68 » Sat Oct 10, 2015 10:47 am

Hint:
2i3j, 2k3 and 2m3n is 2max(i,k,m)3max(j,ℓ,n).
WHUK

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