largenumber

For example I want to calculate (reasonably efficiently) 2^1000003 mod 12321 And finally I want to do (2^1000003 - 3) mod 12321. Is there any feasible way to do this? Basic modulo properties tell us that 1) a + b (mod n) is (a (mod n)) + (b (mod n)) (mod n) , so you can split the operation in two steps 2) a * b (mod n) is (a (mod n)) * (b (mod n)) (mod n) , so you can use modulo exponentiation (pseudocode): x = 1 for (10000003 times) { x = (x * 2) % 12321; # x will never grow beyond 12320 } Of course, you shouldn't do 10000003 iterations, just remember that 2 1000003 = 2 * 2 1000002 , and 2

I haven't really used variance calculation that much, and I don't know quite what to expect. Actually I'm not too good with math at all. I have a an array of 1000000 random numeric values in the range 0-10000. The array could grow even larger, so I use 64 bit int for sum. I have tried to find code on how to calc variance, but I don't know if I get correct output. The mean is 4692 and median is 4533. I get variance 1483780.469308 using the following code: // size is the element count, in this case 1000000 // value_sum is __int64 double p2 = pow( (double)(value_sum - (value_sum/size)), (double)2

Resolution: It turns out there is (probably) "nothing wrong" with the code itself; it is just inefficient. If my math is correct, If I leave it running it will be done by Friday, October 14, 2011. I'll let you know! Warning: this may contain spoilers if you are trying to solve Project Euler #3. The problem says this: The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? Here's my attempt to solve it. I'm just starting with Java and programming in general, and I know this isn't the nicest or most efficient solution. import java.util

I'm developing a class for large number arithmetic, it now knows how to do addition, handle cin and cout. It, however has very limited and basic subtraction functionality, and does not know how to handle negative. But that can be easily resolved. My question is this, how to do multiplication. I will detail how it handle cin and cout here. For cin, it will save integers to value[500], for example, 50 will be saved to value[498] and value[499]. BUT NOT value[0] and value[1] For cout, it will scan for the first non-zero value from value[0] to value[499], and then output from that non-zero value

I have being doing some problems on the Project Euler website and have come across a problem. The Question asks,"Work out the first ten digits of the sum of the following one-hundred 50-digit numbers." I am guessing there is some mathematical way to solve this but I was just wondering how numbers this big are summed? I store the number as a string and convert each digit to a long but the number is so large that the sum does not work. Is there a way to hold very large numbers as a variable (that is not a string)? I do not want the code to the problem as I want to solve that for myself. vid I