Number Theory Worksheet 3–Enhancing Thinking Skills Using BYOD
Testing Fermat’s Conjecture using Mathway on BYOD
Steve and Reta read about a famous French mathematician named Fermat. One of Fermat’s
favourite conjectures was: “ Every whole number is the sum of two, three or four square
numbers.
Steve and Reta discuss Fermat’s idea: Steve said it works for lots of numbers. For example:
14 = 9 + 4 + 1, 27 = 25 + 1+1, 42 = 25 +16 +1. Reta said that there is another way of
working out 42 and it is 42 = 36 + 4 + 1 +1. So there is more than one way of writing a whole
number as the sum of square numbers.
Does Fermat’s conjecture work for all whole numbers up to 100? Why don’t you try for a
few numbers first?
32 =
46 =
15 =
79 =
57 =
83 =
36 =
94 =
Fermat (1601-1665)
For larger numbers you can google Mathway.com and check if a number is a square
number. For example, once you are on the Mathway webpage, click on Algebra, and write
36. Then scroll down the arrow and click on ‘determine if the number is a perfect square’
for the answer. Is the conjecture true for the following numbers?
487 =
10132 =
13458 =
Did the person sitting next to you write the answer in a different way?
Choose some more numbers and find out if there is more than one way of writing a whole
number in terms of square numbers.
M. Nataraj, Selwyn College 2014
M. Nataraj, Selwyn College 2014