Diophantus of Alexandria

Let no problem be deemed too difficult until every avenue has been explored.

The pursuit of knowledge is its own reward.

We must not fear the unknown, but embrace it as an opportunity.

The power of algebra lies in its ability to generalize.

Observe the patterns, for they hold the key to understanding.

Every solution opens the door to new questions.

The journey of discovery is often more rewarding than the destination.

To simplify is to clarify.

Let us proceed with logic and precision.

The foundations of mathematics are built on careful reasoning.

I have merely scratched the surface of what is possible.

The pursuit of truth is a torch passed from generation to generation.

Let us not be content with mere approximation, but strive for exactness.

His boyhood lasted 1/6 of his life; his beard grew after 1/12 more; he married after 1/7 more; his son was born 5 years later; the son lived to half his father's age; and the father died 4 years after his son.

Find three numbers such that the product of any two added to the third is a square.

To find three numbers such that the sum of any two is a square.

To find three numbers such that if from each the next following be subtracted, the remainders are squares.

To find two numbers such that their sum and the sum of their squares are given numbers.

To find three numbers such that the product of any two added to the third is a square, and the sum of all three is a square.

To find three numbers such that the sum of any two is a square, and the sum of all three is a square.