Splitting of Hermitian Forms over Group Rings.
Let be a fixed positive integer. A Lucas -pseudoprime is a Lucas pseudoprime for which there exists a Lucas sequence such that the rank of in is exactly , where is the signature of . We prove here that all but a finite number of Lucas -pseudoprimes are square free. We also prove that all but a finite number of Lucas -pseudoprimes are Carmichael-Lucas numbers.
We prove that every Sturmian word ω has infinitely many prefixes of the form UnVn3, where |Un| < 2.855|Vn| and limn→∞|Vn| = ∞. In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.