By Paul Hoffman

ISBN-10: 0449217507

ISBN-13: 9780449217504

An creation to the delights and demanding situations of recent arithmetic.

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Extra info for Archimedes' Revenge: The Joys and Perils of Mathematics

Sample text

Imagine the sequence of consecutive numbers n! + 2, n! + 3, n! + 4, and so on all the way to n! + n. Now, the first term in the sequence, n! + 2, is evenly divisible by 2; the second term, n! + 3, is evenly divisible by 3; the third term, n! + 4, is evenly divisible by 4; and so on. There are n - I numbers in this sequence, and none is a prime number. By choosing n to be as large as you want, you can have a prime-free sequence of consecutive whole numbers as long as you want. Prime-rich sequences, however, are also abundant.

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Yellow cows = ('/6 + 1/7) white herd. " Stripped to its mathematical essentials, the problem so far is to solve seven equations that involve eight unknowns (four groups of bulls specified by color and four groups of cows of corresponding color). It turns out that these equations are not hard to solve. Indeed, they admit infinitely many solutions, the smallest involving a total herd of 50,389,082 cattle, a number that could comfortably graze on Sicily's 6,358,400 acres. Archimedes, however, did not stop there.