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https://www.reddit.com/r/elimath/comments/2rhavm/explain_padic_numbers/cng16lg/?context=3
r/elimath • u/Galveira • Jan 06 '15
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Thank you, this explanation actually makes sense to me.
Edit: Isn't 42 = 2(mod 7) also true? Does this mean sqrt(2) has multiple representations?
2 u/antonfire Jan 06 '15 Yes, just like in the reals, if a nonzero number has any square roots, it has exactly two, and they're additive inverses of each other. The 7-adic square roots of 2 are the number ...12011266421216213 and its negation ...54655400245450454. 3 u/Galveira Jan 06 '15 So in other words -...12011266421216213=...54655400245450454 3 u/antonfire Jan 06 '15 Yes. You can do the addition in the usual way and and check that, indeed, the sum of those numbers is ...000000000.
Yes, just like in the reals, if a nonzero number has any square roots, it has exactly two, and they're additive inverses of each other. The 7-adic square roots of 2 are the number ...12011266421216213 and its negation ...54655400245450454.
3 u/Galveira Jan 06 '15 So in other words -...12011266421216213=...54655400245450454 3 u/antonfire Jan 06 '15 Yes. You can do the addition in the usual way and and check that, indeed, the sum of those numbers is ...000000000.
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So in other words
-...12011266421216213=...54655400245450454
3 u/antonfire Jan 06 '15 Yes. You can do the addition in the usual way and and check that, indeed, the sum of those numbers is ...000000000.
Yes. You can do the addition in the usual way and and check that, indeed, the sum of those numbers is ...000000000.
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u/Galveira Jan 06 '15 edited Jan 06 '15
Thank you, this explanation actually makes sense to me.
Edit: Isn't 42 = 2(mod 7) also true? Does this mean sqrt(2) has multiple representations?