Timeline for Representing integers as sums of three powers
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2023 at 19:08 | comment | added | Bogdan Grechuk | Yes, that is why the smallest non-trivial cases are n equal to 2 and -2, as indicated in the question. | |
| Jan 8, 2023 at 2:57 | comment | added | Tomita | When $n=a^3$ then $x^4+y^3=z^2+n$ has a trivial solution $(x,y,z)=(b,a,b^2)$ | |
| Jan 5, 2023 at 5:42 | comment | added | individ | There is a similar equation. artofproblemsolving.com/community/c3046h1048092 There is only one problem with such equations. The degree of the equations is large. There are very few independent parameters. As a result, it is impossible to write a formula - because there can be a finite number of solutions. For a given number. The only way out is to guess some combination that will simplify the equation, but this is not always possible. There are few independent variables. | |
| Jan 4, 2023 at 19:02 | comment | added | Will Jagy | quick note, there are infinitely many $n,$ positive and negative, for which $x^2 + y^2 = z^9 + n$ has no solution. | |
| Jan 4, 2023 at 18:00 | history | asked | Bogdan Grechuk | CC BY-SA 4.0 |