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3
votes
1answer
16 views

Predicting how long the result of a permutation

We're calculating the result of a 'tweaked' Birthday Problem, but when we're calculating, we stumped by a very nasty permutation. $$10^{576}P_{10^{16}}$$ Which, make us stop working at the number, ...
0
votes
1answer
81 views

Divisibility of huge numbers

Please help me to solve my homework ;) Prove that for any positive integer $n$ a square of rather big number divides even more huge number: $${\LARGE \left.\underbrace{33\dots 3}_{1\underbrace{00\dots ...
0
votes
1answer
35 views

Find the biggest number from given data below

Maths problem : $$(9^{62773} + 2)^{83721}$$ Now here is the rest of the problem. After finding the huge number I have to find its digital sum. If you don't know what that means just give me the ...
3
votes
0answers
69 views

Transfinite Knuth-arrow hierarchy vs. fast-growing hierarchy

Suppose Knuth arrow notation (and hence the hyperoperation sequence) is extended to transfinite ordinal indices as follows: Let μ be a large countable ordinal such that a fundamental sequence is ...
3
votes
0answers
281 views

Magnitude of $10 \uparrow \uparrow \uparrow 10$

Is there any way to understand the magnitude of $$10 \uparrow \uparrow \uparrow 10$$ ? I know that the number can be constructed as follows : $$M_1 := 10$$ $$M_2 := 10^{10^{10^{...10}}}$$ ...
3
votes
0answers
312 views

First $n$ digits of Graham's Number

I know using Euler's Totient function, it's easy to find the last $n$ digits of Graham's number (or any large repeating power tower), but is there any known way to find the first $n$ digits of ...
2
votes
0answers
76 views

First digits of extremely large numbers (Generalization of “first digits of Graham's number”)

I found a question about the first digits of Graham's number and would like to generalize it : We want the first n digits of the number $a\uparrow^b c$. Which method is the most effective to do ...
2
votes
0answers
63 views

Improving Montgomery product

I am reading the paper "A Cryptographic Library for the Motorola DSP56000" (http://link.springer.com/content/pdf/10.1007%2F3-540-46877-3_21.pdf) which describes a trick to speed-up calculation of the ...
1
vote
0answers
73 views

Tim Chow's proof that the moser-number is much smaller than grahams number

The link here shows a proof from Tim Chow that the moser-number is much smaller than grahams number. I do not understand the inequality 3^^...^^3 (3^^^^^3×2-1 arrows) << G 2 What does G 2 ...
0
votes
0answers
38 views

Monotony of the function $a\uparrow ^b c$ in all the arguments

I want to prove the following monotony properties of hyper-operations : 1) $ a \uparrow^b c < (a+1) \uparrow^b c$ for all $a,b,c \ge 1$ 2) $ a \uparrow^b c < a \uparrow^b (c+1)$ for all $a\ge ...
0
votes
0answers
45 views

Bounds for $(10 \uparrow \uparrow 257) \uparrow \uparrow \uparrow (10 \uparrow \uparrow 257)$

A lower bound of 2[6] (Steinhaus-Moser-Notation) is $$ M:= (10 \uparrow \uparrow 257) \uparrow \uparrow \uparrow (10 \uparrow \uparrow 257)$$ I would like to bound M in the following way : $$10 ...
0
votes
0answers
24 views

Bounds for a sequence and the steinhaus-moser-numbers

Let $(a_k)$ be the following sequence $$a_1=n\ ,\ a_{n+1}=a_n^{a_n}\ for\ all\ n \ge 1$$ It is easy to show $a_k > n\uparrow \uparrow k$ for all $k > 2$. But is it true that $a_k < n ...
0
votes
0answers
35 views

monotony for conway chains

Let X and Y be chains, m and n be natural numbers with 0 < m < n. Is it always true that $$X \rightarrow m \rightarrow Y < X \rightarrow n \rightarrow Y$$ ? I need this to bound the ...
0
votes
0answers
49 views

Tight bounds for the number “2 in a hexagon” wanted (Steinhaus-Moser-Notation)

The Steinhaus-Moser-function is defined in the following way : $$M(n,1,3) = n^n$$ $$M(n,1,p+1) = M(n,n,p)$$ for all $p\ge3$ $$M(n,m+1,p) = M(M(n,1,p),m,p)$$ for all $p\ge3$ and $m\ge1$ The ...
0
votes
0answers
40 views

Potential values of minimum cost maximum flow algorithm

I have a simple directed graph $G(V,E)$ that has a source $s$ and sink $t$. Each edge $e$ of $G$ has positive integer capacity $c(e)$ and positive integer cost $a(e)$. I am trying to find the minimum ...