# infinite group

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## infinite group

[′in·fə·nit ′grüp]
(mathematics)
A group that contains an infinite number of distinct elements.
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(In case of other infinite groups this strategy is not well-defined.
For any positive integer k [greater than or equal to] 3, there exist infinite group positive integers
Jozsef Sandor  proved that for any positive integer k [greater than or equal to] 2, there exist infinite group positive integers ([m.sub.1], [m.sub.2], ...
The main purpose of this paper is using the elementary method and the Vinogradov's important work to prove the following conclusion: For any positive integer k [greater than or equal to] 3, there exist infinite group positive integers ([m.sub.1], [m.sub.2], ..., [m.sub.k]) such that the equation Se ([m.sub.1] + [m.sub.2] + ...
The main purpose of this paper is using the elementary method to prove that for each k [greater than or equal to] 4, there exist infinite group positive integers ([m.sub.1], [m.sub.2], ...
For example, Jozsef Sandor  proved that for any positive integer k [greater than or equal to] 2, there exist infinite group positive integers ([m.sub.1], [m.sub.2], ...
In this paper, we using the elementary method to study this problem, and prove that for any integer n [greater than or equal to] 1, the inequality has infinite group positive integer solutions ([x.sub.1], [x.sub.2], ..., [x.sub.n]).
has infinite group positive integer solutions ([m.sub.1], [m.sub.2], ..., [m.sub.k]).
For any integer k [less than or equal] 2, we can find infinite group numbers [m.sub.1],[m.sub.2], ..., [m.sub.k] such that:
For any integer k [greater than or equal to] 2, we can find infinite group numbers [m.sub.1], [m.sub.2], ...

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