Wieferich's Theorem (other)
Wieferich's theorem may refer to one of the following results named after Arthur Wieferich: * Wieferich's criterion for the solubility of the "First Case" of Fermat's Last Theorem * The solution to Waring's problem In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural numb ...

Arthur Wieferich
Arthur Josef Alwin Wieferich (April 27, 1884 – September 15, 1954) was a German mathematician and teacher, remembered for his work on number theory, as exemplified by a type of prime numbers named after him. He was born in Münster, attended the University of Münster (1903–1909) and then worked as a school teacher and tutor until his retirement in 1949. He married in 1916 and had no children. Wieferich abandoned his studies after his graduation and did not publish any paper after 1909. His mathematical reputation is founded on five papers he published while a student at Münster: *. *. *. *. *. The first three papers are related to Waring's problem. His fourth paper led to the term ''Wieferich prime'', which are p such that p^2 divides 2^(p-1) - 1." See also * Wieferich pair * Wieferich's theorem *Wieferich prime In number theory, a Wieferich prime is a prime number ''p'' such that ''p''2 divides , therefore connecting these primes with Fermat's little theorem, which st ...
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Wieferich's Criterion
In number theory, a Wieferich prime is a prime number ''p'' such that ''p''2 divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime ''p'' divides . Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem, at which time both of Fermat's theorems were already well known to mathematicians. Since then, connections between Wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as Mersenne and Fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original definition of a Wieferich prime. Over time, those connections discovered have extended to cover more properties of certain prime numbers as well as more general subjects such as number fields and the ''abc'' conjecture. , the only known Wieferich primes are 1093 and 3511 . Equivalent definitions The strong ...
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