Since there are infinite primes p, so there exist

infinite group positive integers ([m.sub.1], [m.sub.2] ..., [m.sub.k]) satisyfying the equation

Whether there exist infinite group positive integers ([m.sub.1], [m.sub.2]) such that SJ [m.sub.1] + [m.sub.2]) = [S.sub.c]([m.sub.1]) + [S.sub.c][m.sub.2])?

Since there are infinite prime p, so there exist infinite group positive integers ([m.sub.1], [m.sub.2], [m.sub.k]) such that the equation

For any positive integer k [greater than or equal to] 5, there exist infinite group positive integers ([m.sub.1], [m.sub.2], ...

Whether there exist infinite group positive integers ([m.sub.1], [m.sub.2], [m.sub.3], [m.sub.4]) such that the equation

For any fixed positive integer n [greater than or equal to] 1, the inequality (1) has infinite group positive integer solutions ([x.sub.1], [x.sub.2], ..., [x.sub.n]).

Therefore, the inequality (1) has infinite group positive integer solutions ([x.sub.1], [x.sub.2], ..., [x.sub.n]).

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.

has infinite groups positive integer solutions ([m.sub.1], [m.sub.2],..., [m.sub.k]).

Jozsef Sandor [5] proved for any positive integer k [greater than or equal to] 2, there exist infinite groups of positive integer solutions ([m.sub.1], [m.sub.2],..., [m.sub.k]) satisfied the following inequality:

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

infinite groups positive integer solutions ([m.sub.1], [m.sub.2],..., [m.sub.k]) satisfied the following inequality: