1.2 Algorithm for GCD The Euclidean algorithm is a simple algorithm for finding the gcd of two numbers. The basis of the algorithm is the fact that if a = qb+ c, a, q, b, c ∈ Z,⇒ (a, b) = (b, c). (4) This is very easy to see. Let s = (a, b)⇒ s|a, s|b⇒ a = sa1, b = sb1 t = (b, c)⇒ t|b, t|c⇒ b = tb2, c = tc2 Also c = a− qb = s(a1 − qb1)⇒ s|c Also as s|b (as s is the gcd of (a, b), s divides b and...

Diverticular disease of the colon is a common disease, and its incidence is increasing gradually. A giant colonic diverticulum (GCD) is a rare entity and is defined as a diverticulum greater than 4 cm in size. It mainly arises from the sigmoid colon, and possible etiology is a ball-valve mechanism permitting progressive enlargement. A plain abdominal X-ray can be helpful to make a diagnosis ini...

Temporal lobe epilepsy (TLE) is often accompanied by granule cell dispersion (GCD), a migration defect of granule cells in the dentate gyrus. We have previously shown that a decrease in the expression of reelin, an extracellular matrix protein important for neuronal positioning, is associated with the development of GCD in TLE patients. Here, we used unilateral intrahippocampal injection of kai...

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

Let S = {x1, x2, . . . , xn} be a set of distinct positive integers such that gcd(xi, xj) ∈ S for 1 ≤ i, j ≤ n. Such a set is called GCD-closed. In 1875/1876, H.J.S. Smith showed that, if the set S is “factor-closed”, then the determinant of the matrix eij = gcd(xi, xj) is det(E) = ∏n m=1 φ(xm), where φ denotes Euler’s Phi-function. Since the early 1990’s there has been a rebirth of interest in...