Timeline for Elementary results with p-adic numbers
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2016 at 15:11 | comment | added | Ingo Blechschmidt | It's nice that even a primary-school pupil, maybe armed with a calculator, can verify that $\mathbb{Z}_{10}$ is not an integral domain. Namely, such a child might wonder: Is there a number $x$ such that the last few digits of $x^2$ coincide with those of $x$? $5$ is an obvious first choice, but more digits are possible: $25$ ($25^2 = 625$), $625$ ($625^2=390625$), $90625$ ($90625^2 = 8212890625$), and so on. These approximations actually describe a single $10$-adic number $x$ which satisfies the identity $x^2=x$, or equivalently $x(x-1)=0$. Since $x$ is neither zero nor one, the claim follows. | |
| Nov 20, 2011 at 23:33 | history | answered | user19414 | CC BY-SA 3.0 |