Quandaries
and Queries 

My name is John,
and I'm from Sweden (so pardon my English). Enough of that and to
the question, [level: secondary] (i guess). I
I have earlier searched for patterns in small sums in order to 

John, If you have access to
a unix or linux system, you can make a file called fbb containing
then type
After 15 minutes or longer you will have the result in the file obb (of size 3569863). As you can see, big exponents yield numbers with many digits. For instance,
a number with more than 3 million digits. It is easy to compute the last few digits using modular arithmetics and "repeated squaring'':
so these are the correct last nine digits. However, to compute the whole result, you need memory space to store your answer and all the intermediate calculations, and this is a lot of reading and writing on memory, not counting computations. Claude 

