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What is the remainder when 19^((19^19) - 2) is divided by 10^10? Thanks for help.

 Oct 26, 2019
 #1
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You are right! This is a very tough problem and no ordinary calculator can handle such big exponents, because (19^19) - 2 =1,978,419,655,660,313,589,123,977 - which is 25-digit Prime Number !!.

 

However, if your class takes computer coding, it can be handled by writing a short computer code to do the calculation for you. Out of curiosity, I wrote the following code in Python to give you the answer to your question:

 

%%time
# Fast python code that first calls pow()  
# then applies % operator
import math as m
a =19
b =(19 ** 19) - 2 
p =10000000000  
# Using direct fast method to compute  
# (a ^ b) % p. 
d = pow(a, b, p) 
print("The Remainder =", f"{d :,d}")  
The Remainder = 7,185,569,139 - This is the answer to your question.
Wall time: 981 µs

 Oct 26, 2019
 #2
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Thanks guest,

 

Was this a coding question - I suspect it was.

If so you should have said so int the question.

 Oct 26, 2019

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