Help challenging numbers

[alaric]

Hi,

I try to solve a mathematical question (just for fun, and someone (in my family) who claims it can't be done, must be proven wrong) I like this challange (or am I just a fool)

what is it;
try to display the outcome of 4444 ^ 4444

This is huge, and Im strugling with it. Because ie 1000 ^1000 give an outcome of "infinity"

My start question is:
how to store these big values? (a double is a bit too small)

the challange goes furter. but I try to solve this first.

anyone, who can help me in this math challenge?

 

[cjard]

it's like, 7mod9, or something...

i've seen this problem before, or similar, and i suspect that you will ask next, once 4444^4444 is calculated, you will seek to know what's the sum of the digits of the sum of the digits of the sum of the digits of it?

have ou seen these sites:
http://www.math.utk.edu/~denzler/M351-Sp2004/hints24.pdf
http://www.artofproblemsolving.com/Forum/topic-31409.html

 

[alaric]

Yep you're right.
(it seems to be one of the math classics)

Thanks for pointing me to the answer.
But is there a way to crack this nut the hard way? To actualy program a calculator that can handle these enormeous numbers?
(I probably mis the bigger picture here......)

thanks in advance

 

[cjard]

hmm, those sites point to the workings that will get to the answer too. i think the main inference is that these numbers are so huge as to be impossible to feasibly compute, but the point being that you dont have to do the calc. often in science we say that the correct way is the right answer with the least work..

treating it from a pure pragma aspect; you would need a very big hard disk to store the number generated by 4444^4444. it would be hard to calculate if only from this regard, that you'd struggle to find a medium to store the numbers while you worked on them.. this usually leads mathematicians to find an easier answer