Date of Award

Fall 2018

Document Type


Degree Name

Master of Science



First Advisor

Dr. Andrius Tamulis

Second Advisor

Dr. Dianna Galante

Third Advisor

Dr. J. Christopher Tweddle


Fermat's Last Theorem sat unproven for more than 300 year. It all started around 1637, when Pierre de Fermat stated the theorem: xp + yp = zp has no positive integer solutions for x, y, z when p > 2. He wrote a note in the margin saying that he has the proof but it was bigger than the margin. Sophie Germain, a French mathematician tried her hand in proving Fermat's Last Theorem. She came up with a theorem that was later reference to as Germain Theorem. She took Fermat's Last Theorem xp + yp = zp and suggested that if p is a prime number greater than 2 and 2p + 1 is prime also, then p must divide x, y, or z. Germain's theory and proof changed the approach to proving Fermat's Last Theorem and divided it into two cases where the first case states that none of the three values x, y, or z is divisible by p, and the second case states that the exponent p divides at least one of the three values x, y, or z. The main concept of this paper is to explore Germaine's approach to solving Fermat's Last Theorem for the exponent p > 2 and how her idea led to solving the problem by introducing a new and fresh approach.