Using Fermat's little theorem, find the least residue of the multiplicative inverse of 5^53 - 4 modulo 53.

Q: xplain why F, contains a primitive nth root of unity if and only if p = 1 mod n. int: Use the…

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Q: Prove 10^47+67 is not a prime(use Fermat's). Thank you :)

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Q: True or false: If p is an odd prime, then (p-1)! + 2^(p-1) congruent 0(mod p). Justify your answer.

A: p is an odd prime.

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: for 3^800 how can I find the last digits of it by using mods (such as last digit and 2nd last…

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Q: Give the polynomial for the base 16 expansion of a natural number. Include restric- tions for…

A: To give the polynomial for base 16 expansion of a natural number. p(b)=ckbk+ck-1bk-1+...+c1b1+c0,…

Q: ou are told that 159238479574729 = 529

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Q: Compute the prime factorization of:                     gcd(75, 90)                     75 = 3 · 52…

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Q: Use Fermat’s Little Theorem to prove that 8^46 − 1 is divisible by 139

A: Use Fermat’s Little Theorem to prove that 8^46 − 1 is divisible by 139

Q: Find the prime factorization of a number 23256. Show Work. Write this factorization in a canonical…

A: Given number is 23256 To find the prime factorisation of the number. And to write in canonical form.…

Q: The multiplicative inverse of r*+x-1 in Z,[x]/ is: X^3 X+1 x^4 None

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Q: (x^6)+(x^5)+(x^4)+1 least one of the answers above is NOT correct of the questions remains…

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Q: Y OU (a) Find the least residue of 639 modulo 10. (b) Use Fermat's little theorem to find the least…

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Q: (7) Using the Euclidean algorithm find the multiplicative inverse of 253 mod 600 in Z600-

A: a=251,  n=600. Consider 600=2 . (253)+ 94 253=2 . (94)+ 65 94 = 1 . (65)+29 65=2. (29)+ 7 29= 4 (7)+…

Q: Let x = 1234500123450012345 (usual decimal representation). What is the remain- der of x when…

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Q: Use Euler's Theorem to compute and reduce 4^1226(mod 35).

A: To solve 41226mod 35 using Euler's Theorem.   Euler's theorem states that if gcda,n=1 then, aϕn≡1mod…

Q: how do i use Euler's thm to find the value? 3242 mod 385

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Q: Use the pigeonhole principle to prove that the decimal expansion of a rational number min eventually…

A: To Prove:  Using the pigeonhole principle that the Decimal expansion of a rational number m/n…

Q: True or False. Briefly explain why.  The least nonnegative residue of −123 modulo 12 is 3.

A: We recall the definition.

Q: 2. Find 52019 (mod 13).

A: Here,given  52019(mod 13)Now we find 52019(mod 13) using Chinese Remainder Theorem and Fermat's…

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: Apply the Fast Modular Exponentiation to find 0 ≤M <7, where 315 EM mod 7.

A: Note that, we can write 315 = 32×5×7. Therefore we get that 7 divides 315.

Q: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

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

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Q: Using Euler's theorem, find the least residue of the multiplicative inverse of  5^phi(121) - 4…

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Q: Use Hensel’s Lemma and Chinese Remainder Theorem to find all solutions to x^2 + 3x + 17 ≡0 (mod 300)

A: Introduction: Hensel’s Lemma is a powerful tool in number theory that allows us to lift solutions of…

Q: olve and answer the following problems as indicated. 2) Create the multiplication table for…

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Q: 5 =5 Hence, 6"-1 is divisible by 5 is (10.). for n=1 Part 2: Assume that 6" - 1 is divisible by 5…

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Q: Q2: Use Fermat's method to analyze the number into its prime factors (1745)

A: We have to find prime factorisation of 1745 using Fermat's method.

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

A: Given: We have to compute

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

A: jyujhjyukjhjkkhjjghfgf