Timeline for Can every positive integer eventually be expressed in this form?
Current License: CC BY-SA 4.0
6 events
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| May 20 at 22:43 | history | edited | John Omielan | CC BY-SA 4.0 |
Make a few more minor fixes, clarifications and other changes.
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| May 20 at 20:24 | comment | added | John Omielan | @lookatme (cont.) expressed in that form", I assume you mean certain values as sums of them, i.e., the 4, 10 and 16 I mentioned. I got around that by determining values sufficiently ahead of each $a_1$, as I explained in my paragraph about using induction. It's somewhat of an outline, rather than providing all of the specific details, which I hope you can now handle yourself instead. | |
| May 20 at 20:20 | comment | added | John Omielan | @lookatme Adding $d_k$ to create the specified numbers comes from changing the appropriate $s_k$ power values from $1$ to $2$. For example, to get $8 = d_0 + d_1$, we change both $s_0$ and $s_1$ from $1$ to $2$. By "repeating powers", I assume you mean using a $d_k$, for a specific value of $k$, more than once. Of course, that is generally a problem, although there are examples of the same value being different differences of powers, e.g., $6=3^2-3=2^3-2$. Nonetheless, this is why I specifically ensured each $d_k$ value is used at the most once. Finally, regarding "some $d_n$ cannot be ... | |
| May 20 at 20:11 | comment | added | look at me | Can you specify how adding $d_n$ creates numbers that can be expressed in this form? Repeating powers may be a problem. (And the fact that some $d_n$ cannot be expressed in that form) | |
| May 20 at 15:57 | history | edited | John Omielan | CC BY-SA 4.0 |
Add an overall summary to my first sentence, and several more details. Also, make a few minor corrections (e.g., parity related) and other changes (e.g., switch indices to be from highest to lowest).
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| May 20 at 6:25 | history | answered | John Omielan | CC BY-SA 4.0 |