Timeline for sums of digits of powers of integers
Current License: CC BY-SA 4.0
16 events
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| Sep 22, 2019 at 1:39 | history | edited | user6976 | CC BY-SA 4.0 |
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| Sep 22, 2010 at 2:56 | comment | added | user6976 | @Joseph: Shorey and Tijdeman mention results of Senge and Straus, and C.L.Stewart, at the end of Chapter 12 of their book ``Exponential diophantine equations". | |
| Sep 21, 2010 at 3:56 | history | edited | user6976 | CC BY-SA 2.5 |
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| Sep 20, 2010 at 16:04 | history | edited | user6976 | CC BY-SA 2.5 |
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| Sep 20, 2010 at 14:01 | comment | added | user6976 | I think somebody erased one of my comments here - the one where I explain a connection with exponential Diophantine equations. | |
| Sep 20, 2010 at 13:07 | history | edited | user6976 | CC BY-SA 2.5 |
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| Sep 20, 2010 at 13:01 | history | edited | user6976 | CC BY-SA 2.5 |
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| Sep 20, 2010 at 2:28 | comment | added | user6976 | @Gerry: Yes, it is correct according to MathSci. Also you may find in Stewart's paper a double exponential estimate for $f$. I have not been able to find better estimates in the literature although there exist much more recent papers on the subject generalizing Stewart's results, in particular. Calculations suggest a linear bound. | |
| Sep 20, 2010 at 1:07 | comment | added | Gerry Myerson | The references in full: C L Stewart, On the representation of an integer in two different bases, J Reine Angew Math 319 (1980) 63-72, MR 81j:10012; H G Senge, E G Straus, PV-numbers and sets of multiplicity, Proceedings of the Washington State University Conference on Number Theory (1971) 55-67, MR 47 #8452. | |
| Sep 19, 2010 at 13:29 | history | edited | user6976 | CC BY-SA 2.5 |
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| Sep 18, 2010 at 16:34 | comment | added | user6976 | @Joseph: I changed the references. | |
| Sep 18, 2010 at 16:32 | history | edited | user6976 | CC BY-SA 2.5 |
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| Sep 18, 2010 at 14:26 | history | edited | user6976 |
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| Sep 16, 2010 at 16:52 | comment | added | user6976 | By the way, for $a=2$ or $5$, there is an old result of A. Schinzel, which is included in Sierpiński's "250 problems in elementary number theory". If I remember the proof correctly, this result shows that in this case $f$ grows at most linearly. | |
| Sep 16, 2010 at 16:05 | comment | added | Joseph O'Rourke | @Mark: Just for my own education, could you identify in which Shorey-Tijdeman paper this is established? They have written quite a few papers together... | |
| Sep 16, 2010 at 13:03 | history | asked | user6976 | CC BY-SA 2.5 |