Taro Morishima
Encyclopedia
was a Japanese
mathematician
specializing in algebra
who attended University of Tokyo
in Japan
. Morishima published at least thirteen papers, including his work on Fermat's Last Theorem
. and a collected works volume published in 1990 after his death. He also corresponded several times with American
mathematician H. S. Vandiver
.
Japanese people
The are an ethnic group originating in the Japanese archipelago and are the predominant ethnic group of Japan. Worldwide, approximately 130 million people are of Japanese descent; of these, approximately 127 million are residents of Japan. People of Japanese ancestry who live in other countries...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specializing in algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
who attended University of Tokyo
University of Tokyo
, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
. Morishima published at least thirteen papers, including his work on Fermat's Last Theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
. and a collected works volume published in 1990 after his death. He also corresponded several times with American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician H. S. Vandiver
Harry Vandiver
Harry Schultz Vandiver was an American mathematician, known for work in number theory.He was born in Philadelphia, Pennsylvania to John Lyon and Ida Frances Vandiver...
.
Morishima's Theorem on FLT
- Let m be a prime number not exceeding 31. Let p be prime, and let x, y, z be integerIntegerThe integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s such that xp + yp + zp = 0. Assume that p does not divide the productProduct (mathematics)In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication...
xyz. Then, p² must divide mp − 1-1.