Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.

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A set of integers whose elements all divide $2015^{200}$ but do not divide each other

Let $S$ be a set of natural numbers,such that each element divides $2015^{200}$ but for no two elements $a$ and $b$, $a|b$. Find the maximum number of elements in $S$ . $2015^{200}=(5\cdot ...
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Find all positive integers $n$ for some given condition.

Find all positive integers $n>1$ such that $n^2$ divides $2^n+1$ I found that $n$ is of the form $6k+3$.
3
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Different methods to multiply

The sum and the multiplication in $\mathbb{Z}_p$ correspond to the the sum and the multiplication of powerseries. Example for sum: $$(3 \cdot 7^0+4 \cdot 7^1+2 \cdot 7^2)+(5 \cdot 7^0+3 \cdot 7^1)= ...