Question

Use Fermat's Little theorem to solve: 6^400 (mod 37)

Use Fermat's Little theorem to solve: 6^400 (mod 37)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Fermat's Little theorem : If p is a prime number, then for any integer a, the number is an integer multiple of p that is .

Since is a prime number and is an integer so by Fermat's Little theorem ,

  

[ raising power to 11 ]

[ multiplying both side by 64 ]

Hence is

Answer : 1 .

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that for any integer a, a^37 is congruent to a (mod 1729). We have Fermat's...
Prove that for any integer a, a^37 is congruent to a (mod 1729). We have Fermat's Little Theorem and Euler's Theorem to work with.
Use Fermat's Little Theorem to compute the following remainders for 44824482 (Always use canonical representatives.) 4^482=...
Use Fermat's Little Theorem to compute the following remainders for 44824482 (Always use canonical representatives.) 4^482= ? mod 5 4^482 = ? mod 7 4^482= ? mod 11 Use your answers above to find the canonical representative of 4482 mod 3854482 mod 385 by using the Chinese Remainder Theorem. [Note 385=5⋅7⋅11385=5⋅7⋅11 and that Fermat's Little Theorem cannot be used to directly find 4482 mod 3854482 mod 385 as 385 is not a prime and also since it is larger than...
Is 4^3072 - 9^4824 divisible by 65? use fermat's little theorem. Make sure to show every...
Is 4^3072 - 9^4824 divisible by 65? use fermat's little theorem. Make sure to show every work. Especially solving 9^24 mod 65 = 1
can we use fermat's little theorem to prove a number is prime?
can we use fermat's little theorem to prove a number is prime?
Number Theory use a.) Fermat's theorem to verify that 17 divides (11^104) + 1 b.) Euler's...
Number Theory use a.) Fermat's theorem to verify that 17 divides (11^104) + 1 b.) Euler's theorem to evaluate 2^1000 (mod 77)
Using Fermat’s Little theorem, find the multiplicative inverse of 4 in mod 13. Show your work....
Using Fermat’s Little theorem, find the multiplicative inverse of 4 in mod 13. Show your work. Using Euler’s theorem, find 343 mod 11.
Prove Fermat’s Little Theorem using induction: ap ≡ a (mod p) for any a ∈Z.
Prove Fermat’s Little Theorem using induction: ap ≡ a (mod p) for any a ∈Z.
Using Chinese Remainder Theorem solve for X: x = 2 (mod 3) x = 4 (mod...
Using Chinese Remainder Theorem solve for X: x = 2 (mod 3) x = 4 (mod 5) x = 5 (mod 8) I have the answer the professor gave me, but I can`t understand what`s going on. So if you could please go over the answer and explain, it would help a lot. x = 2 (mod 3) x = 3a + 2 3a + 2 = 4 (mod 5) (2) 3a = 2 (2) (mod 5) -----> why number...
(20 pts) Use construction approach in the proof of the Chinese Remainder Theorem to solve system...
(20 pts) Use construction approach in the proof of the Chinese Remainder Theorem to solve system of congruences ? ≡ 2 (mod 3) and ? ≡ 1 (mod 4) and ? ≡ 3 (mod 5).   
Use Wilson's Theorem to show that 79! (mod 83)
Use Wilson's Theorem to show that 79! (mod 83)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT