Prouhet-Tarry-Escott problem

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In mathematics, the Prouhet-Tarry-Escott problem asks for two distinct sets of m integers each, A and B, such that:

for each integer k from 1 to n.

For example, for m = 4 and n = 3, a solution is the two sets {492, 276, 618, 834} and {294, 438, 816, 672}, because:

492¹ + 276¹ + 618¹ + 834¹ = 294¹ + 438¹ + 816¹ + 672¹

492² + 276² + 618² + 834² = 294² + 438² + 816² + 672²

492³ + 276³ + 618³ + 834³ = 294³ + 438³ + 816³ + 672³.

This problem was named after Prouhet, who studied it in early 1850s, and Tarry and Escott, who studied it in early 1910s.

[edit] External links

• Prouhet-Tarry-Escott problem
• Eric W. Weisstein, Prouhet-Tarry-Escott problem at MathWorld.