# Diophantus of Alexandria/Arithmetica/Book 3

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## Problems by Diophantus of Alexandria:

## Problems by Diophantus of Alexandria: *Arithmetica* Book $\text {III}$

### Problem $6$

To find $3$ numbers such that their sum is a square and the sum of any pair of them is a square.

That is, let $\set {p, q, r}$ be a set of $3$ natural numbers such that:

What are those $3$ numbers?

### Problem $12$

To find $3$ numbers such that the product of any $2$ of them added to the $3$rd gives a square.

That is, let $\set {p, q, r}$ be a set of $3$ natural numbers such that:

What are those $3$ numbers?