Discussion and Homework
Seventh Reading Assignment

Notes for the Readings

Definition VII.13: A composite number is that which is measured by some number.

Definition VII.14: Numbers composite to one another are those which are measured by some number as a common measure.

Questions for Discussion

1. Diophantus knows the rules for multiplying a "minus" by a "minus" and a "minus" by a "plus", yet the biography of Diophantus states that he accepted only positive rational roots. Why might you need to know the rules rules for multiplying a "minus" by a "minus" and a "minus" by a "plus" to solve equations even if you only accept positive solutions?
2. What do you think Diophantus would call x⁷, x⁸, x⁹and x¹⁰?

1. In IV. 29, does x²2 + x+ 1/4 come out of nowhere? Why does Diophantus use this particular perfect square trinomial?
2. In IV. 30, does x² - x + 1/4 come out of nowhere? Why does Diophantus use this particular perfect square trinomial?

Homework Problems

1. Divide 25 and 36 into two squares using Diophantus' method.
2. Use Diophantus' method to find four square numbers such that their sum added to the sum of their sides is 73.
3. Use Diophantus' method to find four square numbers such that their sum minus the sum of their sides is 15.
4. Prove that if 3 measures an odd number k times, then 3 measures the odd number "two places removed" k + 2 times.
5. Prove that if 5 measures an odd number k times, then 3 measures the odd number "four places apart" k + 2 times.

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