How to compute modulo power of big integers?

Question

How to compute modulo power of 10,000 digit number to 10,000 digit number using C language
Eg:-(1234567891111123433434^211222324334343422233)%**********

And how to store and retrieve such a large values

Comments

I hope I understood your problem correctly, see the following mathematical properties -
a^n mod x = (a mod x)^n mod x
a^n mod x = (a^2 mod x)^(n/2) mod x
Any many similar operations

Now the problem can be solved using mix of modulo properties...Let me know if this is fine then we can write the program...

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What if n <= 10^10000 ?

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You can always do by breaking the mod operation
say n = n1*n2

a^n mod x = (a^n1 mod x)^n2 mod x

Answer 1

As Salil suggested say you have following problem -
(a1 ^ a2) mod n

Step 1: Replace a1 with mod value i.e. and initialize result as 1

a1 = a1 mod n  
result = 1

Step 2: Find out the prime factor of a2 say

a2 = n1 * n2 * n3 ....

Step 3: for each factor (for each i)

result = result * (a1^ni mod n) 

Comments

Thanks Deepak and Salil for your valuable comments
I have a doubt
can we even reduce a2 to a2 mod (n)??
Now how to implement these with c program
Please help me out

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No mod can not be applied on a2.