Take two rows of respective length m and n:(adsbygoogle = window.adsbygoogle || []).push({});

a_{1}, a_{2}, a_{3},..., a_{m}and b_{1}, b_{2}, b_{3}, ..., b_{n}.

Then produce as follows the generated array G_{ai}to contain these elements:

a_{1}, a_{1}+a_{2}, a_{1}+a_{2}+a_{3}, ..., a_{1}+..+a_{m},

a_{1}+..+a_{m}+a_{1}, a_{1}+..+a_{m}+a_{1}+a_{2}, .....

Alike produce the generated array G_{bj}to contain these elements:

b_{1}, b_{1}+b_{2}, b_{1}+b_{2}+b_{3}, ..., b_{1}+..+b_{n},

b_{1}+..+b_{n}+b_{1}, b_{1}+..+b_{n}+b_{1}+b_{2}, ....

The numbers a_{i}and b_{j}are cumulated cyclically to produce their respective arrays G_{ai}and G_{bj}.

Two questions are open to be analyzed (by me) - hope someone has a hint:

1. How to express analitically all numbers contained in G_{ai}U G_{bj}as a function.

2. Since the rows a_{i}and b_{j}has periods m and n respectively, what is the resulting period of the superposition , ie. the period of G_{ai}U G_{bj}?

I appreciate your comment or hint.

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# Period of superposed cyclic integer rows

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