Exponential Diophantine equations - MSP

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(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

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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