Student Organizer #5: Extending the Idea of Pythagorean Triples
The Proof of the Century!
Print this page to help you complete the activities below:
1. Using a scientific calculator, try to find numbers that satisfy the following equations:a^{3} + b^{3} = c^{3} a^{4} + b^{4} = c^{4} a^{5} +b^{5} = c^{5} a^{10} + b^{10} = c^{10}
2. How does changing the exponents in the above formulas affect your results? Is there an a, b, and c that work for all of the above equations?
3, Does it matter?
4. Do your experiences mean that you have a mathematical proof?
5. How would one go about proving such an idea?
