Fermat and Goldbach
Your name:
1. Fermat’s Last Theorem
“If n is a positive integers greater than 2, then it is impossible to find positive integers x, y,
and z such that xn + y n = z n .”
For many years, mathematicians attempted to find counterexamples to this “Theorem”.
One possibility that was put forth was the following:
178212 + 184112 = 192212
(1) Using only the definitions of even and odd integers, explain why this equation cannot
be true.
2. Goldbach’s Conjecture
“Every even integer greater than 2 can be written as the sum of two prime numbers.”
(1) Test this conjecture on three positive integers greater than 10.
(2) Do you think the conjecture is true?