## Collatz ... again

Maple 13

Hi everybody,

The Collatz conjecture can be used to give students a taste of a topic in Number Theory.  See the Wikipedia article for a good explaination.

https://en.wikipedia.org/wiki/Collatz_conjecture

Also, a conjecture is something that is probrably true.  Enjoy my little Maple procedure.  (in .mw and .pdf forms)

Collatz_third_time.mw

Collatz_third_time.pdf

Matt

## Modular Arithmetic...

How do I use msolve to solve y^2 + y - 11=0 in Zp for all primes p with 41=< p =<107 ?

Also, using the results make a conjecture describing the primes p for which there are solutions to y^2 + y - 11 = 0 in Zp

This was what I did.

41<=p<=107

msolve(y^2 + y - 11=0, p)

but I received this error, no implementation of msolve matches the arguments in call, msolve(y^2 + y - 11=0, p)

Any help is appreciated. Thanks

## Calculating Collatz's Conjecture ...

Hi everyone, I'm trying to print out Collatz's Conjecture's steps for any given value with the following code but it takes forever and prints nothing. Any idea on how I can get it working ?

checkCollatzValue:=proc(val) local res, remaining;
while res <> 1 do
remaining = irem(val, 2); remaining;
if remaining = 0 then res = val / 2; else res = val * 3 + 1; fi;
res;
od;
end proc;

## Conjecture sequence problem...

I'm having problem dealing with this question on Maple and would appreciate any help possible.

If f(x) = x/2, if x is even
f(x) = 3x-1, if x is odd

which sequence will 2013^1102 fall in
1->1->1...
5->7->5...
17->25->37->55->41->61->91->17...

Thanks!

## A list of small graphs, invariants and conjectured...

by: Maple

A list of small graphs with associated pictures and tables of
values of various graph invariants.

The graph invariants were made using Maple programs which uses
the networks and GraphTheory packages.

A picture presents some inequality conjectures between the graph invariants.

http://www.msci.memphis.edu/~speeds/

Sam Speed   August 29, 2011

## MRB constant rational?A

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