A book claims the following statement, "if in a region of space magnetic field is unidirectional, then at every point of space it must be uniform in magnitude also". Is this true? I feel like I'm missing something, because if we consider a current carrying wire then the magnitude is not uniform however it is unidirectional for a region of space. Even if I use the maxwell's equations I'm just able to show that the magnetic field will be constant wrt to the direction in which its pointed...
Hmm. Thanks for the help. I'll follow along your steps to see what I get. The answer I believe is 4R, which is why I believed there might be some short and neat method to get it done.
Hey. I have a question. We have that $1<a_1<a_2 < \dots < a_{18} < 77$. We define $A = \{1,a_1, a_2, \dots, a_{18}, 77\}$ and that $B = \{x + y | x,y \in A\}$ and we're given that $B$ has exactly $39$ elements. Is it necessary that the $a_i$'s are in arithmetic progression? I have identified that $B=\{2, 78, 154, 1+a_1, 1+a_2, \dots, 1+a_{18}, 77 + a_1, 77+a_2 , \dots 77+a_{18}\}$ since all these elements are distinct and formed by taking sums of some two elements in $A$.
@nickbros123 i believe it is actually quite elementary, I hope I'm not overlooking something.. $x^k \equiv 1 \pmod p$. Then the multiplicative order $\operatorname{ord}_p(x) \mid k$ and also $\operatorname{ord}_p(x) \mid p-1$. Then $\operatorname{ord_p(x)} \mid \gcd(p-1,k)=1$, which means $\operatorname{ord}_p(x) = 1$ and so $x\equiv 1 \pmod p$.
Hey. Does anyone know a proof that $x^k - 1 \equiv 0 \pmod p$, where $p$ is a prime and $k$ a positive integer coprime to $p-1$, has the only solution $x\equiv 1 \pmod p$?
@Integreek my teachers were also saying the exam was quite lengthy. i've not gone through the complete paper yet, just math, and I found quite a few time consuming questions, esp. in paper 2
@RakshithPL He did give some details about some months back. His JEE story is insane. His math hard-carried him throughout JEE. He's for math and math is for him
it's such a tragedy for the world's oldest democracy, with its highest elected executive proclaiming himself king on social media with supports justifying it as "trolling libs"
@User1865345 he should've been investigated then, no? investigate him, and if he's indeed some Russian asset then at least don't let him run for the position thrice
I don't understand why Trump being American, would go to such limits to undermine every one of his allies and support Russia whenever possible. Its as if Russia has something on Trump. This is really appalling.
If something like this happened in our country, the entire bureaucratic system would go on strike and government functioning would probably come to a halt.
I'm not American, and being an outsider I was more receptive to Trump's overall campaign -- no biological men in female sports, no illegal immigration, etc. But this whole DOGE this is so insane and crazy.
In the search of a question
In the search of a question
