Question

6. Use properties of congruences to calculate $10^{6,000,000,000,000,000,000,000,000,000,000,000,000,000,002} \mod 13$? (the exponent has 43 digits).

          6. Use properties of congruences to calculate
$10^{6,000,000,000,000,000,000,000,000,000,000,000,000,000,002} \mod 13$? 
(the exponent has 43 digits).

6. Use properties of congruences to calculate
10^6,000,000,000,000,000,000,000,000,000,000,000,000,000,002 13?
(the exponent has 43 digits).

Added by Catalina C.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Sri K

01/28/2023

Step 1

Step 1: Since we are looking for the remainder when 10^(6,000,000,000,000,000,000,000,000,000,000,000,000,002) is divided by 13, we can use Euler's theorem which states that if a and n are coprime (which is the case for 10 and 13), then a^(phi(n)) ≡ 1 (mod n), Show more…

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Use properties of congruences to calculate 10^(6,000,000,000,000,000,000,000,000,000,000,000,000,000,002)mod13? (the exponent has 43 digits). 6. Use properties of congruences to calculate (the exponent has 43 digits)