Let a be a natural number such that gcd(a, 10) = 1. Use Euler’s theorem to prove that a^40n+1 and a must have the same ones and tens digits in their base ten expansions

Q: Which of [0], [1], [2], [3], [4] is equal to [3]^2023 in Z_5? What is [15]^1989 congruent to in…

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Q: Let a and b be integers with GCD(a, b) = d and let a = da', b = db'. Prove that GCD(a', b')=1

A: and  be integer such that .It is given that  and .We have to prove .Note: According to the…

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

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Q: find the amount of odd three-digit numbers that can be created. (

A: here given digits are  [0, 1, 2, 3, 4, 5, 6]. so there are total 7 digits . here use counting…

Q: Give a construction of a field with 16 elements.

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Q: Find the order of all element of Z8 under addition mod . Please brieflt explain and show all the…

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Q: Use four terms of Newton's binomial expansion to approximate 11.

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

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Q: a be an odd integer. Pro

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Q: Let f= (14723 5 6) and g = (1 5 3 264) be permutations in S. What is the second line of fin two-line…

A: Introduction: Permutation businesses are mathematical businesses whose individuals are permutations…

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: (4) Apply the Fast Modular Exponentiation to find 0 < M < 87, where 5015 = M mod 87.

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Q: Find the normalized binary representation (in a 32 bit computer) of x = -0.7908. (if x = 0, contact…

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Q: Va 占>0 !! に

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Q: nsist only of of even length. Generalize to find the EGF number of ations that consist only of…

A: To find: (1) The EGF for the number of permutations that consist only of cycles of even length.…

Q: Using Fermat's little theorem, find the least residue of the multiplicative inverse of 5^53 - 4…

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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: If gcd(7, a) = 1, prove that either a +1 or a – 1 is divisible by 7. 20

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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: 15-1mod 17 (use Fermat theorem)

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

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: Compute (7^3)^161 (mod 250)

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Q: write a program to evaluate even numbers for [1,10],and [11,20]respectively in matlab

A: Even numbers for [1,10] is given below-

Q: Find 2's complement of 001011011001100

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Q: Find [7]^-1 in Z55 under multiplication.

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Q: Use the Euler Theorem to calculate 17^81(mod 55)

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Q: Find the order of 175 in Z_245

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Q: Convert (11000 0110 0011₂ from its binary expansion to hexadecimal expansion.

A: In this question, the concept of the Number System is applied. Number System A number system is a…

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

A: jyujhjyukjhjkkhjjghfgf

Q: Let a, b and c a=1b=0C=9 example with enrolment number 001054321, you would take a = 0, b = 5 and c…

A: The answer to the given question is provided below with respective explanation.

Q: Prove that 18000 + 28000 38000 Theorem (and not a calculator). 18000 + 58000 + +4° 8000 is a…

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Q: If a₁, a2, a3, a4 are the coefficients of any four consecutive terms in the expansion of (1 + x)",…

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Q: Give the ring of integers and discriminants of the following number fields. Q(e^(2*pi*i)/7)

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Q: Find the mod of (2-4i)^1/2

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