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Apr
12
awarded  Popular Question
Feb
25
awarded  Popular Question
May
18
awarded  Popular Question
Mar
7
awarded  Yearling
Mar
8
accepted Show that $a^n \mid b^n$ implies $a \mid b$
Mar
8
comment Show that $a^n \mid b^n$ implies $a \mid b$
Didn't find anything in the search.
Mar
8
asked Show that $a^n \mid b^n$ implies $a \mid b$
Mar
8
comment Proof that (n!+1,(n+1)!+1)=1
Ah okay, thanks!
Mar
8
accepted Proof that (n!+1,(n+1)!+1)=1
Mar
8
comment Show that 13 divides $2^{70}+3^{70}$
@Arturo: Nice, I didn't know about \pmod. Thanks!
Mar
8
comment Show that 13 divides $2^{70}+3^{70}$
Oooh yeah! Division works because inversion works, which only works for mod p, p is prime. Correct?
Mar
8
comment Show that 13 divides $2^{70}+3^{70}$
Thanks! Walking through it like that was very helpful to figure out just what kinds of operations are allowed with congruences. Thanks!
Mar
8
awarded  Commentator
Mar
8
accepted Show that 13 divides $2^{70}+3^{70}$
Mar
8
comment Show that 13 divides $2^{70}+3^{70}$
Aah. I knew I could add them up easily but was coming from the wrong direction, trying to do it backwards. Thanks for clearing that up!
Mar
8
comment Show that 13 divides $2^{70}+3^{70}$
@Arturo Alright. :) Thanks for editing it for me!
Mar
8
comment Proof that (n!+1,(n+1)!+1)=1
Ah wait. $n! + 1 \equiv 0$ means $n! \equiv -1$? I can just do that, just as if the $\equiv$ were an =? That n! is congruent to both 0 and -1 makes no sense in my head though....
Mar
8
comment Proof that (n!+1,(n+1)!+1)=1
Hm, I don't see how n! is also congruent to -1. Could you expand on that? Thanks for the encouragement! I am just an engineer, so this one class will probably all the number theory I will learn, unless I end up inventing error correcting codes at my job. I am enjoying it though!
Mar
8
comment Proof that (n!+1,(n+1)!+1)=1
Could you explain how you know that m divides (n+1)∗(n!+1)−(n+1)!+1?
Mar
8
comment Show that 13 divides $2^{70}+3^{70}$
Argh, typo! Should be 3^70. Same exponent, different base. Thanks!