Least residue of 8^68 modulo 17

Q: 15!/14! *

A:

Q: Find the index of 12Z in 3Z

A: The integers are

Q: Use Fermat's little theorem to find the least residue of 8^70 modulo 23

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the order of 5 modulo 2^100.

A:

Q: Consider a product of an odd prime with itself and represent it as a sum of two squares. 1. 13^2 =…

A: According to question given:Product of an odd prime with itself and represent it as a sum of Two…

Q: Find all integers n such that (n^2) - 1 is prime.

A: n² - 1 = (n-1)(n+1)  Now, if (n² - 1) needs to be a prime, then, either n-1 is equal to 1 or, n+1 is…

Q: prove that 3^n is greater than n^3 for all n greater than or equal to 4

A:

Q: Find a primitive root modulo 2 * 19^2022

A: Consider the number n=2×192022. We know that a primitive root of modulo n is an integer g such that…

Q: Find the first 3 mon-Zerw terms orf the Mnelaurin. derres

A:

Q: Find all whole#s that leave remainder 3 upon division by 5?

A: The solution is given below:

Q: d) limnoo 1 •k=1 an e) limn 1 48x = =공 6 4

A:

Q: Compute phi(6^2 x 4^3). (Note that this is not a prime power factorization.)

A:

Q: Least residue of 45^37 mod 19 when using Fermats Little Theorem

A:

Q: Compute sigma(2^3 x 5^2 x 4^2).

A: Given: We have to compute

Q: Let c = 2^100 and p be the smallest prime such that p >= c. How many composite numbers are between c…

A: Let c=2100 And p=min p is prime:p≥c,p∈ℤ Claim: Total number of composite number between c & p,…

Q: How many zeroes does 188! end with?

A: count number of five's in 188, 5*2=10 . Divide 188 and write quotient again divide quotient again by…

Q: Find the 7-adic expansion of 1/2 up through the 7^3 power

A: jyujhjyukjhjkkhjjghfgf

Q: 5. Let (S2, A, Pr) be an abstract probability space, and let A, B be events. Prove that Pr(B|A) +…

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Q: Prove that n-5 is odd iff n^2-1 is odd

A: Please check step 2 for the solution.

Q: Prove that 2^? +3^? is a multiple of 5 for all odd ?∈N.

A: We will solve this problem using principle of mathematical induction.

Q: -1

A: No it is not a prime numbers

Q: Express 5^7 using base e

A: From the given information the given expression is:

Q: Least residue of 63^9 mod 10

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: how did they get 9x^2 from (x^4)/(5x^2)mod11 ?

A: Use of z11[x],

Q: 1^3+2^3+3^3+...n^3 = [n(n+1)/2]^2

A:

Q: Find the least residue of 13^456 (mod 31)

A: Solution