Allan Macleod

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We consider the problem of determining a rational point (x, y), of infinite order, on the elliptic curve y 2 = x 3 + ax 2 + bx. The well-known method of 4-descent has proven very effective, and we give explicit formulae for the various stages. For points of large height, however, there can still be a significant search to be done. We describe a very simple(More)
Low breeding success has been associated with declines in population and range of the re-introduced Capercaillie Tetrao urogallus in Scotland. Annual breeding success from 26 Scottish forests surveyed between 1991 and 2009 averaged only 0.6 chicks per female, the lowest rate recorded in 16 previous studies. Reduced breeding success was due to proportionally(More)
We discuss the problem of finding distinct integer sets {x 1 , x 2 ,. .. , x n } where each sum x i + x j , i = j is a square, and n ≤ 7. We confirm minimal results of Lagrange and Nicolas for n = 5 and for the related problem with triples. We provide new solution sets for n = 6 to add to the single known set. This provides new information for problem D15(More)
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