Let K=Fq be an elliptic function eld. For every natural number n we determine the number of prime divisors of degree n of K=Fq which lie in a given divisor class of K.

For an optimal elliptic curve E over Fq(t) of conductor p·∞, where p is prime, we show that E(F )tor is generated by the image of the cuspidal divisor group.

We study $S$-adic shifts generated by sequences of morphisms that are constant-length. call a sequence constant-length torsion-free if any prime divisor one the lengths is infinitely many lengths. show

AdigraphC is called a zero divisor if there exist non-isomorphic digraphs A and B for which A×C ∼= B ×C , where the operation is the direct product. In other words,C being a zero divisormeans that cancellation property A×C ∼= B×C ⇒ A ∼= B fails. Lovász proved that C is a zero divisor if and only if it admits a homomorphism into a disjoint union of directed cycles of prime lengths.Thus any digra...

Assumption We’ll make the following “learning divisor with noise” assumption: LDN Assumption: let P a random n bit prime, R a random n4 bit prime, and let N = PR. A distinguisher that is given N and X1, . . . , Xpoly(n) cannot distinguish between case (I) Xi’s are chosen independently at random from [N ], and (II) Xi = PQi + 2Ei (mod N) where Qi is chosen independently at random from [R] and Ei...

Let R be a commutative ring and let ? Z n the zero divisor graph of id="M2"> R , whose vertices are nonzero divisors id="M3"> such that two id="M4"> u , v adjacen...