I doubt that Wingeer is implying that. What he might be getting at is the following:drama2 said:firstly thanks very much for responding. in regards to ur question the remainder would be a 1000. i assume you are implying that this is also the remainder for 10^100 mod 1001 though i can't figure out why that is the case and ift its not too much trouble would you please explain cos I am too stupid to be frank to see the connection :)
No, that's not the correct remainder since 10≢-10 (mod 1001).drama2 said:therefore10^100=-10mod1001
from this would it be correct that the remainder is 10?
10^100 mod 1001 is a mathematical expression that represents the remainder when 10^100 is divided by 1001. In other words, it is the number that is left over after dividing 10^100 by 1001.
Finding the remainder of 10^100 mod 1001 can help solve certain mathematical problems, such as finding the last digit of a large number or determining patterns in number sequences. It is also used in encryption algorithms and other applications in computer science.
To calculate the remainder of 10^100 mod 1001, you can use the exponentiation by squaring method. First, divide the exponent (100) by 2 and take the remainder (0). Then, square the base (10) and take the remainder when divided by 1001 (100). Repeat this process until the exponent is 1, and then multiply all the remainders together. In this case, the remainder of 10^100 mod 1001 is 1.
Yes, there are faster methods such as Euler's totient theorem or the Chinese remainder theorem. These methods use mathematical concepts and properties to simplify the calculation and reduce the number of steps needed.
Aside from its use in mathematics and computer science, finding the remainder of 10^100 mod 1001 is also used in fields such as cryptography, number theory, and coding theory. It has practical applications in data compression, error correction, and data security.