Document
... Fermat's Last Theorem Fermat's Last Theorem states that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2. ...
... Fermat's Last Theorem Fermat's Last Theorem states that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2. ...
15(1)
... / = 0, 1, 2, 3, 4 but composite for / = 5, 6. It is an unsolved problem whether or not 22' + 1 has other prime values. We note in passing that, when k = 2,F6=8 = 23, and 8m ± 1 = (23 ) ^ ± 1 = (2m ) 3 ± 7 is always composite, since A 3 ± B is always factorable. It is th ought that Fg + 1 is a prime. ...
... / = 0, 1, 2, 3, 4 but composite for / = 5, 6. It is an unsolved problem whether or not 22' + 1 has other prime values. We note in passing that, when k = 2,F6=8 = 23, and 8m ± 1 = (23 ) ^ ± 1 = (2m ) 3 ± 7 is always composite, since A 3 ± B is always factorable. It is th ought that Fg + 1 is a prime. ...
Full text
... MacMahon [1], pp. 217-223, studied special kinds of partitions of a positive integer, which he called perfect partitions and subperfect partitions. He defined a perfect partition of a number as "a partition which contains one and only one partition of every lesser number" and a subperfect partition ...
... MacMahon [1], pp. 217-223, studied special kinds of partitions of a positive integer, which he called perfect partitions and subperfect partitions. He defined a perfect partition of a number as "a partition which contains one and only one partition of every lesser number" and a subperfect partition ...
1 (mod n)
... ab=1 (mod (n)), we have ab = t(n)+1, for t>=1 Suppose that x in Zn*; then we have (xb)a = xt(n)+1 (mod n) = (x(n))tx = 1tx (mod n) = x (mod n) As desired. For x in Zn but not in Zn*, (do exercise) ...
... ab=1 (mod (n)), we have ab = t(n)+1, for t>=1 Suppose that x in Zn*; then we have (xb)a = xt(n)+1 (mod n) = (x(n))tx = 1tx (mod n) = x (mod n) As desired. For x in Zn but not in Zn*, (do exercise) ...
L. ALAOGLU AND P. ERDŐS Reprinted from the Vol. 56, No. 3, pp
... by the result proved in §2, that the exponent to which 2 divides the superabundant n determines the exponents of all other primes with an error of 1 at most . S . Pillai, in his paper On o-_1 (n) and 0(n), Proceedings of the Indian Academy of Sciences vol . 17 (1943) p . 70, refers to certain result ...
... by the result proved in §2, that the exponent to which 2 divides the superabundant n determines the exponents of all other primes with an error of 1 at most . S . Pillai, in his paper On o-_1 (n) and 0(n), Proceedings of the Indian Academy of Sciences vol . 17 (1943) p . 70, refers to certain result ...
List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.Some reasons why a particular publication might be regarded as important:Topic creator – A publication that created a new topicBreakthrough – A publication that changed scientific knowledge significantlyInfluence – A publication which has significantly influenced the world or has had a massive impact on the teaching of mathematics. Among published compilations of important publications in mathematics are Landmark writings in Western mathematics 1640–1940 by Ivor Grattan-Guinness and A Source Book in Mathematics by David Eugene Smith.