Since there are infinite primes p, so there exist

infinite group positive integers ([m.

For any fixed positive integer n [greater than or equal to] 1, the inequality (1) has infinite group positive integer solutions ([x.

Therefore, the inequality (1) has infinite group positive integer solutions ([x.

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apply the complexity of non-commutative groups to public key cryptography, assess the generic-case performance of various algorithms, and explore the asymptotically dominant properties of

infinite groups used in public key cryptography.

Groups, graphs, and trees; an introduction to the geometry of infinite groups.

He takes a modern, geometric approach to group theory, which is particularly useful in the study of infinite groups, focusing on Cayley's theorems first, including his basic theorem, the symmetry groups of graphs, or bits and stabilizers, generating sets and Cayley graphs, fundamental domains and generating sets, and words and paths.

He describes some new techniques that make the computations more accessible for finite and some

infinite groups.

This collection of 17 papers comes from the 1999 meeting at Bielefeld of experts on interactions between mostly

infinite groups on the one hand and topological, combinatorial and arithmetic structure on the other.

has

infinite groups positive integer solutions ([m.

Jozsef Sandor [7] proved for any positive integer k [greater than or equal to] 2, there exist

infinite groups positive integer solutions ([m.