Waring Experiments
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Ivars Peterson (MathLand)  
You might suspect that, at some point, four squares would no longer be enough to express a given whole number. This reasonable supposition was overturned in seventeenth century, when Pierre de Fermat proved that every positive whole number can be expressed as a sum of at most four squares. In 1777, Edward Waring, a practicing physician and mathematics professor at the University of Cambridge, conjectured that something similar could be proved for cubes, fourth powers, and so on. He stated, without proof, that it would take the sum of at most 9 cubes or 19 fourth powers to express any whole number.  


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