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http://worldcat.org/entity/work/id/1862841766

The Chinese Remainder Problem and Polynomial Interpolation

The Chinese Remainder Problem (Ch. R.P) is to find an integer x such that x = a sub i(mod m sub i) (i=1 ..., n), where mi are pairwise relatively prime moduli and a sub i are given integers. In the 1950's I learnt orally from Marcel Riesz that the CH. R.P. is an analogue of the polynomial interpolation problem P(x sub i) = Y sub i(i=1 ..., n), P(x) is a subset of pi sub n-1, and that the Ch. R.P. can be solved by an analogue of Lagrange's interpolation formula. The author now adds the remark that the Ch. R.P. can be solved, even more economically, by an analogue of Newton formula using successive divided differences.

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  • "The Chinese Remainder Problem (Ch. R.P) is to find an integer x such that x = a sub i(mod m sub i) (i=1 ..., n), where mi are pairwise relatively prime moduli and a sub i are given integers. In the 1950's I learnt orally from Marcel Riesz that the CH. R.P. is an analogue of the polynomial interpolation problem P(x sub i) = Y sub i(i=1 ..., n), P(x) is a subset of pi sub n-1, and that the Ch. R.P. can be solved by an analogue of Lagrange's interpolation formula. The author now adds the remark that the Ch. R.P. can be solved, even more economically, by an analogue of Newton formula using successive divided differences."@en
  • "The Chinese Remainder Theorem is one of the most important results of elementary Number Theory as it was used by Kurt Goedel in one of his most fundamental papers in Logic. The paper uses the analogy with the theorem of polynomial interpolation to solve it in two different ways."@en

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  • "The Chinese Remainder Problem and Polynomial Interpolation"@en

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