k=l Fermat's little theorem says that if p is a prime, then kP-l 3 lmodp for k = 1,.. .,p-1. Therefore, for each prime p, Sp--lmodp. The question becomes: Does there xist a non-prime n such that Sn 3â€¦ (More)

In response to a letter from Goldbach, Euler considered sums of the form âˆž âˆ‘ k=1 ( 1 + 1 2m + Â· Â· Â· + 1 km ) (k + 1)âˆ’n for positive integers m and n. Euler was able to give explicit values forâ€¦ (More)

We consider the functional equation f(t) = 1 b b?1 X =0 f t ? a for all t 2 IR; (F) where 0 < a < 1, b 2 IN n f1g and ?1 = 0 1 : : : b?1 = 1 are given parameters, f : IR ! IR is the unknown. We showâ€¦ (More)

BACKGROUND
Penetrating thoracic injury is commonly found in South Africa. A review of our recent experience was undertaken to assess the effectiveness of our protocols for this type of injury.
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We construct Lipschitz functions such that for all s > 0 they are s{HH older, and so proximally, subdiierentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitzâ€¦ (More)

We examine a certain class of Schauder bases for the space C[âˆ’1, 1] consisting of algebraic polynomials orthogonal with respect to the Chebycheff weight of the first kind. We give an improvedâ€¦ (More)