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**11**

votes

**1**answer

600 views

### Are there infinitely many natural numbers not covered by one of these 7 polynomials?

Consider the following polynomials:
$$
f_1(n_1, m_1) = 30n_1m_1 + 23n_1 + 7m_1 + 5\\
f_2(n_2, m_2) = 30n_2m_2 + 17n_2 + 13m_2 + 7\\
f_3(n_3, m_3) = 30n_3m_3 + 23n_3 + 11m_3 + 8\\
f_4(n_4, m_4) = ...

**4**

votes

**1**answer

160 views

### Cover of a n-simplex with balls

Consider a n-simplex. For each edge (i,j), consider a n-ball, such that vertices i and j are antipodal on this ball. Is the simplex covered by the union of these balls? Thank you.