![\text{(i)}](/media/m/2/f/5/2f54b8a68ace12cc659644ae3f86b6bd.png)
Odredi sve proste brojeve
![p_1<p_2<...<p_n](/media/m/7/f/5/7f5615a0ade797c13d8bbb7c9336f253.png)
takve da je
![\left( 1+\displaystyle\frac{1}{p_1}\right)\cdot \left( 1+\displaystyle \frac{1}{p_2}\right)\cdot ... \cdot \left( 1+\displaystyle\frac{1}{p_n}\right)](/media/m/b/0/0/b005a697f58056d12dc7af02366c7875.png)
prirodan broj.
![\text{(ii)}](/media/m/e/4/f/e4fa4235bd5d8fd8284e16676a261ad1.png)
Postoje li prirodni brojevi
![1<a_1<a_2<...<a_n](/media/m/d/a/b/dab0a7242a625435760d3e2c8e208b3a.png)
takvi da je
![\left( 1+\displaystyle\frac{1}{a_1^2}\right)\cdot \left( 1+\displaystyle \frac{1}{a_2^2}\right)\cdot ... \cdot \left( 1+\displaystyle\frac{1}{a_n^2}\right)](/media/m/3/5/c/35c54dd65d7d9266d958171c8593b617.png)
prirodan broj.
%V0
$\text{(i)}$ Odredi sve proste brojeve $p_1<p_2<...<p_n$ takve da je $$\left( 1+\displaystyle\frac{1}{p_1}\right)\cdot \left( 1+\displaystyle \frac{1}{p_2}\right)\cdot ... \cdot \left( 1+\displaystyle\frac{1}{p_n}\right)$$ prirodan broj.
$\text{(ii)}$ Postoje li prirodni brojevi $1<a_1<a_2<...<a_n$ takvi da je $$\left( 1+\displaystyle\frac{1}{a_1^2}\right)\cdot \left( 1+\displaystyle \frac{1}{a_2^2}\right)\cdot ... \cdot \left( 1+\displaystyle\frac{1}{a_n^2}\right)$$ prirodan broj.