formalizes and extends a method used by Guy, Lacampagne, and Selfridge in ... (By a recent result of Reese Scott [5], for equations of the form pm+c = q" , the.
Dec 11, 2017 - values of t give all the solutions of the equation. Another ... "Given a Diophantine equation with any number of unknown quantities and with.
balancing and Lucas-balancing numbers and study their solutions. 1. Introduction ..... Using Theorem 4.1, we can find solutions of a Diophantine equation de-.
May 27, 2010 - Kenelm Digby and John Wallis to find all the integer solutions to the equa- ... This correspondence all passed through Digby's hands, and thus.
Special thanks to Dr. Betty K. Nannyonga, Dr. David Ssevviiri and Mr. Alex B. Tumwesigye ... 2.3 Field extensions and algebraic number fields .
In other words, the value of y0 equals the number of non-zero entries in .... 1. What are the best bounds we can give for M0(X) in terms of the generating set X?
(i) For the equation & + 7α = 3c +5d , k = Sb,5b,13b, or 17δ, and for many similar
... 1* Introduction* By an exponential Diophantine equation. (eDe) we mean an ...
Pacific Journal of Mathematics
EXPONENTIAL DIOPHANTINE EQUATIONS J. L. B RENNER AND L ORRAINE L. F OSTER
Vol. 101, No. 2
December 1982
PACIFIC JOURNAL OF MATHEMATICS Vol. 101, No. 2, 1982
EXPONENTIAL DIOPHANTINE EQUATIONS J. L. BRENNER AND LORRAINE L. FOSTER CONTENTS
1. 2. 3. 4. 5. 6. 7. 8. 9.
Introduction Summary Equations of the Form 1 + xa = yb + zc Equations of the form xa + yb = zc + wd Theorems Concerning Equations of the General Form a b c d p +q =r +s α δ C ώ α C ώ The Equations 1 + 2 + 7 = 3 + 5 , 3 + T = 3 + 5 + 2 a b e d Equations of the Form p + q + r = s Problems and Conjectures Index of eDe's Acknowledgment, References
263 265 266 269 283 286 294 297 299 300
We study equations in which the unknowns are the exponents. (Work in this field originated with C. St0rmer and D. H. Lehmer. More recently, Leo J. Alex has extended their results; his work relates to classification of nonahelian simple groups.) α c d b b b δ ( i ) For the equation & + 7 = 3 +5 , k = S ,5 ,13 , or 17 , and for many similar 4-term equations, we find all integral solutions. α δ c
