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How do I find the value of $operatorname{LCM} (a_1^k,a_2^k, ldots ,a_n^k) pmod {m}$?

LCM can be upto or greater than $10^{50}$.$k$ and $m$ are upto $10^9$. My current approach isFinding the LCM .(LCM % m)^k=A.A % m.This is...

1

Mathematics Asked on 2 years ago

What does it mean to write X=Y+W where W is gaussian with mean 0.

Assuming X Y are two random variables. When we write X=Y+W with W~Gaussian(with 0 mean), Do we mean the random variable X-Y ~ Gaussian(with 0 mean)? Or does it mean...

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Mathematics Asked by zhongyuan chen on 2 years ago

Assume $T_n,T$ are bounded bijective linear operators $T_n to T$ pointwise. Show $T_n^{-1}to T^{-1}$ pointwise $iff$ $|T_n^{-1}|leq C$

Assume $T_n,T$ are bounded bijective linear operators $X to Y$ and $T_n to T$ pointwise. Show $T_n^{-1}to T^{-1}$ pointwise $iff$ $|T_n^{-1}|leq C$ Note: ...

1

Mathematics Asked on 2 years ago

When two quadratics seems to output the same values are they necessarily the same?

Joel is thinking of a quadratic and Eve is thinking of a quadratic. Both use $x$ as their variable. When they evaluate their quadratics for $x=1$, they get...

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Mathematics Asked on 2 years ago

$f(X_n)$ converges in probability to $f(X)$ implies $X_n$ converges in probability to $X$

Show that $(X_n)_n$ converges in probability to $X$ if and only if for every continuous function $f$ with compact support, $f(X_n)$ converges in probability to ...

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Mathematics Asked by Kurt.W.X on 2 years ago

An extension field induces new variety

If one have an irreducible affine algebraic varieties $X$, one can define the function field of $X$ as the field of fraction of its coordinate ring $K[X]$....

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Mathematics Asked on 2 years ago

Product of connected sets is connected

I know that this question had already been asked here but there is a problem ... all the proofs that I've seen used homeomorphisms and continuous functions. Well my teacher...

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Mathematics Asked by pipita on 2 years ago

Are all almost virtually free groups word hyperbolic?

Suppose $G$ is a finitely generated group with a finite symmetric generating set $A$. Lets define Cayley ball $B_A^n := (A cup {e})^n$ as the set of...

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Mathematics Asked by Chain Markov on 2 years ago

Finding Terminal Lat/Long with initial lat/long, distance and bearing

So I have these three inputs -Reference Latitude and LongitudeDistance from reference pointBearing (in Radians)Now I'm looking for the Terminal latitude and longitude to plot in my map application. I...

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Mathematics Asked on 2 years ago

An illusionist and their assistant are about to perform the following magic trick

Let $k$ be a positive integer. A spectator is given $n=k!+k−1$ balls numbered $1,2,dotsc,n$. Unseen by the illusionist, the spectator arranges the balls into a sequence as...

2

Mathematics Asked on 2 years ago

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