Unformatted text preview: isnot aninteger. Q.E.D. 6.9. Conclusion of the Proof of 6.2 (6.9.0) Let a, b, c, n be integers, n> 1, and suppose that the hyper- geometric equation with parameters a/n, b/n, c/n has two "rood p" solutions for almost all p (i. e., suppose a/n, b/n, c/n verify (6.2.6)). We must prove that E(a/n, b/n, c/n) has a full set of algebraic solutions (cf. (188.8.131.52)), in order to conclude the proof of 6.2. (6.9.1) As we saw in 6.3, this is the case if any of the exponent differences (184.108.40.206) 1 - c/n, c/n - a/n - b/n, a/n - b/n is an integer. (6.9.2) We thus assume that none of the exponent differences is an integer; then 6.6.0 implies that none of the numbers (220.127.116.11) a/n, b/n, c/n - a/n, e/n - b/n...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
- Fall '11