(*)' Fn = ox. In [1], Cohn solved (*) for c = 1, 2. In [9], we found all solutions of O ) such that <? is prime and either o = 3 (mod 4) or c < 10,000. Harborth & Kemnitz [4] have asked for solutions of (&) for composite values of o. Clearly, it suffices to consider only squarefree values of c. If c < 1000, then c has at most three distinct odd prime factors. Therefore c = kp where p is prime a...

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

Cytotoxic effector T cells of F1 (BALB/c X BALB.B) (H-2d/b) mice immunized against the minor histocompatibility differences of C57BL/10 (H-2b) can lyse targets from C57BL/10, but cannot lyse B10.D2 (H-2d) targets. Despite this lack of cross-reaction in the cytotoxic assay, C57BL/10 cells do prime F1 (BALB/c X BALB.B) mice for a secondary cytotoxic response to B10.D2. C57BL/10-primed, B10.D2-boo...

1. I n t r o d u c t i o n In 1640, Pierre de Fermat conjectured that all numbers F m = 2 2 ' " + 1 for m = 0, 1, 2 , . . . , (1) are prime, which was later found to be incorrect. The numbers Fm are called Fermat numbers after him. If Fm is prime, we say that it is a Fermat prime. Until the end of the 18th century, Fermat numbers were most likely a mathe­ matical curiosity. The interest in the ...

An effective HIV vaccine will most likely require the induction of strong T-cell responses, broadly neutralizing antibodies (bNAbs), and the elicitation of antibody-dependent cellular cytotoxicity (ADCC). Previously, we demonstrated the induction of strong HIV/SIV cellular immune responses in macaques and humans using synthetic consensus DNA immunogens delivered via adaptive electroporation (EP...

The objective of this study was to develop a palatable precooked lamb leg roast. Lamb legs (n = 60) were fabricated into 240 roasts. Roasts were assigned to one of four spice treatments: control (CON), Italian, Mexican, prime rib. After being injected with a 15 percent brine mixture, roasts were smoked to an internal temperature of 63°C, vacuum packaged, and frozen at -10°C. Roasts were thawed ...

Solution 1.1.1. The prime factorization of 720 is 2 · 3 · 5. If we look only at the prime factors of x, y, z, we see that the exponents of 2 in the factorizations of x, y, z must sum to 4, the exponents of 3 must sum to 2, and the exponents of 5 must sum to 0. The number of possible triples (a, b, c) that correspond to the exponents of 2 in the prime factorizations of x, y, z is simply the numb...

1. We say that g(n) is additive if g(mn)=g(m)+g(n) holds for every coprime pairs m, n of positive integers . If, moreover, g(p') =g(p)' for every prime power pa , then g(n) is called strongly additive . By p, pi , p2 , . . ., q, qr , q2 , . . . we denote prime numbers, c, Cl, c2i . . . are suitable positive constants . F(n) and x(n) denote the largest and the smallest prime factor of n . The sy...