MARC Record from marc_columbia

LEADER: 03573fam a2200337 a 4500
001 1446008
005 20220602035839.0
008 931026t19941994mau b 001 0 eng
010 $a 93023740
020 $a0125871708
035 $a(OCoLC)29671943
035 $a(OCoLC)ocm29671943
035 $9AHW5981CU
035 $a(NNC)1446008
035 $a1446008
040 $aDLC$cDLC$dDLC
050 00 $aQA161.E95$bR53 1994
082 00 $a512/.74$220
100 1 $aRibenboim, Paulo.$0http://id.loc.gov/authorities/names/n79065103
245 10 $aCatalan's conjecture :$bare 8 and 9 the only consecutive powers? /$cPaulo Ribenboim.
260 $aBoston :$bAcademic Press,$c[1994], ©1994.
300 $axiv, 364 pages ;$c24 cm
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
504 $aIncludes bibliographical references (p. 331-357) and indexes.
505 0 $aPt. P. Preliminaries. 1. Binomials and Cyclotomic Polynomials. 2. The Cyclotomic Field. 3. The Pythagorean Equation, Special Cases of Fermat's Last Theorem and Related Equations. 4. Continued Fractions. 5. The Equations EX[superscript 2] - DY[superscript 2] = [actual symbol not reproducible]C -- Pt. A. Special Cases. 1. Preliminary Lemmas. 2. The Sequence of Squares or Cubes. 3. The Equation X[superscript m] - Y[superscript 2] = 1. 4. The Result of Stormer on Fermat's Equation. 5. The Attempts to Solve X[superscript 2] - Y[superscript n] = 1. 6. The Equation X[superscript 2] - Y[superscript n] = 1, n [actual symbol not reproducible] 3. 7. The Equations X[superscript 3] - Y[superscript n] = 1 and X[superscript m] - Y[superscript 3] = 1, with m, n [actual symbol not reproducible] 3. 8. The Equation [actual symbol not reproducible]. 9. The Sequence of Powers of 2 or 3. 10. Interlude. 11. The Equation 2X[superscript n] - 1 = Z[superscript 2]. 12. [pi] and Grave's Problem.
505 0 $a13. A Problem of Fermat on Pythagorean Triangles and the Equation 2X[superscript 4] - Y[superscript 4] = Z[superscript 2]. 14. The Equations [actual symbol not reproducible] and [actual symbol not reproducible]. 15. Representation of Integers by Binary Cubic Forms. 16. Some Quartic Equations -- Pt. B. Divisibility Conditions. 1. Getting the Consecutive Powers 8 and 9. 2. The Theorem of Cassels and First Consequences. 3. Prime Factors of Solutions of Catalan's Equation. 4. The Theorem of Hyyro. 5. The Theorems of Inkeri -- Pt. C. Analytical Methods. 1. Some General Theorems for Diophantine Equations. I. The Equation X[superscript m] - Y[superscript n] = 1. 2. Upper Bounds for the Number and Size of Solutions. 3. Lower Bounds for Solutions. 4. Algorithm to Determine the Eventual Solutions. II. The Equation a[superscript U] - b[superscript V] = 1. 5. What Will Be Discussed. 6. Finiteness of the Number of Solutions. 7. Algorithm to Determine the Eventual Solutions.
505 0 $a8. The Largest Prime Factor of Values of Quadratic Polynomials. 9. Effective Results. III. The Equation X[superscript U] - Y[superscript V] = 1. 10. The Theorem of Tijdeman. 11. A Density Result -- Appendix 1. Catalan's Equation in Other Domains. (A). Catalan's Equation over Number Fields. (B). Catalan's Equation over Fields K(t) and Domains K[t]. (C). Catalan's Equation Over Function Fields of Projective Varieties -- Appendix 2. Powerful Numbers. (A). Distribution of Powerful Numbers. (B). Additive Problems. (C). Difference Problems.
650 0 $aConsecutive powers (Algebra)$0http://id.loc.gov/authorities/subjects/sh94000059
852 00 $bmat$hQA161.E95$iR53 1994