# Fermat's Last Theorem

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was noticed. Although Germain had a challenging start to her career, she was persistent, ambitious, and determined; these qualities, as well as her work in mathematics, made her hard to ignore. Sophie Germain began her career by attempting to solve Fermat’s Last Theorem which states that “xn + yn = zn has no positive integer solutions for x, y, z when n > 2” (Riddle). Germain worked relentlessly on proving this theorem and eventually believed had she solved it. Her conclusion was this: “for each odd prime exponent p, there are an infinite number of auxiliary primes of the form 2Np+1 such that the set of non-zero p-th power residues xp mod (2Np+1) does not contain any consecutive integers;” however, her theory was proven wrong shortly after (Riddle). Regardless of her setback, Germain continued to focus on her career and improving her skills in mathematics. Another contribution Germain made to the mathematical world was the theorem she created called Germain’s Theorem, which stated “If p is an odd prime such that 2p + 1 is also prime and if x, y and z are integers none of which is divisible by p then xp + yp , zp. Such x, y and z cannot therefore be counterexamples to Fermat’s Last Theorem for exponent p” (Whitty). Germain’s theorem signified the end of her career in mathematics, however, her work created a foundation for other mathematicians in the future. Once Germain completed her work in mathematics, she moved on to physics. Her inspiration to work on vibrating…

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“Sophie Germain’s Theorem can be applied for many prime exponents, by producing a valid auxiliary prime, to eliminate the existence of solutions to the Fermat equation involving numbers not divisible by the exponent p” (Laubenbacher and Pengelley, 9). Legendre later used Germain’s findings in a supplement to the second edition of his book, Essai sur le Théorie des Nombres (O’Connor and Robertson). The Institut de France awarded Germain a medal for her work on Fermat’s Last Theorem and Germain…

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under the alias of Le Blanc, affianced in correspondent with the author. Sophie Germain was no ivory-tower mathematician, which later became evident in 1807, when French troops were occupying Hanover. Recalling Archimedes’ destiny and dreading for Gausss’s safety in the story she once read, she addressed an inquiry to the French commanding officer, General Pernety, who was a family friend of the Germains. One of Sophie Germain’s theorems is connected to the baffling and still unanswered problem…

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A. Defining Reaction Mechanisms and Catalyst Structure The methane-to-methanol reactions that we aimed to evaluate consist of four critical steps starting from the initial reactants (CH4, NH4+, oxo): C-H activation followed by a hydrogen atom abstraction (HAA) from CH4 to form some combination of the hydrogenated complex, ammonium or ammonia, and a methyl radical; a radical rebound (RR) to form a methanol adduct and ammonium; methanol dissociation from the metal; and catalysis regeneration via…

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standard practices during the time period because he prefers pleasure from sex from unconventional methods over loyal monogamy. Septimus is academically tutoring Thomasina, but is also teaching her sex in a unique manner considering their time period. This introduces Thomasina’s desire for knowledge, but also how sex and mathematics can be a societal battle. Septimus then immediate contrasts sex to math in order to portray how even though they seem like binary oppositions, they are immensely…

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Mathematical proof is a method used in both primary and secondary schools at varying levels. Children should be able to justify and give reasons for a conjecture they have produced in order to validate a mathematical proof. There are various techniques that can be used to illustrate the nature of proof in schools. Mathematical proof is defined as a thorough and believable argument to support the truth of a prediction in maths, which turns the assumptions into valid conclusions (Haylock and…

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next axiom, the nature of the relationship depends on how both parties punctuate the communication sequence. Earlier on in our relationship we were discussing our bills looking towards the future. My wife’s son is 23 and in the Air Force and yet she was still paying for his cellphone. I asked her why she did this and I am not sure if I came off judgmental or what but she quickly snapped back you pay for your daughters. I reminded her that my daughter had graduated high school and was going to…

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that one of the central goals of school mathematics, notably at the upper secondary level, is the development of proof concepts (Coe & Ruthven, 1994). The incorporation of algebraic proofs in Victorian Mathematics education also refutes the criticism that the focus on algebraic proofs theme is sporadic at the secondary school level (Pedemonte, 2008). Many different methods of proof are stated in both the VCE Mathematics Study Design 2016-2018 and some VCE Mathematics textbooks: Specialist…

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are people that will disagree and say that the reason of evolution is because with time our species became more observant and gained knowledge and just knew that these things would work then they created them. I believe that this is completely wrong I think that there needs to be a theory then experiments, that is the only way for evolution to work. People believe that the basis of math is based off of assumptions. And I completely agree because assumptions and theories to me are synonyms.…

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These things don't exist in math. Math is full of "rules" that don't have exceptions. Things such as the Pythagorean Theorem will always work for right triangles. There will never be a right triangle where a^2 + b^2 does not = c^2. This is what I like about math. Math is a subject that I think would never Let me down ; It has no contradictions. It's something that's reliable and useful. I've learned that without math, life would be a cycle of events without reason. If I ever wonder why when I…

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