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In this paper we describe the history of amicable numbers, i.e. pairs of positive integers such that each is the sum of all proper divisors of the other, from their first mention in ancient Greece up to the present. Special attention is given to the results of the two mathematicians who proved important general theorems on amicable numbers, Thābit ibn Qurra and Leonhard Euler. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to review the current state-of-the-art for predicting settlements of shallow foundations in granular soils. The traditional settlement prediction methods are critically reviewed. Present settlement prediction methods generally overestimate the settlements and underestimate the allowable pressures, making the foundation designs very conservative. Some recent developments, including two deterministic methods and a probabilistic approach, are showed as they have significant potential to improve the current state-of-the-art. [ABSTRACT FROM AUTHOR]