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mathhelpforum.com

Kurepa's conjecture states that for any prime number p > 2, we have 0! + 1! + \ldots + (p - 1)! \not\equiv 0 \pmod{p} We let !p denote the expression on the left-hand side. We call it the left factorial of p. We do not know any infinite set of prime numbers for which the conjecture holds...

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mathworld.wolfram.com

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i from x and distance j from y depends only on i, j, and the graph distance between x and y, independently of the choice of x and y. In particular, a distance-regular graph is a graph for which there exist integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly c_i...

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