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

Q: Determine the coefficient of x65 in the full expansion of (x – 2)100. (You need not а. evaluate…

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Q: Briefly explain binary long division

A: Binary Division:- With the exception of base 2, the binary division operation resembles the base 10…

Q: n be a positive natural nun (an)" is equivalent to: 4n Let a) n²n (n²-4n) b) n(n²^_^) d) na^ (^^-2^)…

A: Given, n4n-(2n)2n

Q: In GF(2^8), find the multiplicative inverse of (x^7+x) modulo (x^8 + x^6 + x^5 + x + 1). Use table…

A: The extended Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two…

Q: Of the following, which is the smallest? A) 1.001 x 10^4 B) 1.01 x 10^3 C) 1.01 x 10^2 D) 1.1 x 10^2

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Q: What is the product using Pascal's triangle : (x-1)^10

A: Pascal's triangle is a mathematical concept where each number is the sum of the two numbers directly…

Q: Use the the Binomial Theorem to calculate 11^11 (just giving the end result is not enough.)

A: To find the value of 1111 using the binomial theorem. Now, the Binomial expansion of (1+x)n is:…

Q: Evaluate (6 – 5)^2 by working within the parentheses first. Evaluate 6^2 – 5^2. Compare the answer…

A: Evaluate (6 – 5)^2 Evaluate 6^2 – 5^2.

Q: Use Wilson's Theorem to verify that 4(29!) + 5! is divisible by 31.

A: The given number is 4 (29)! + 5! . Our aim is to verify that the given number is divisible by 31…

Q: Use the Fermat's Theorem to determine the last digit of 12347865435 when divided by 11

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

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Q: Are all perfect squares divisible by 2

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Q: how many different bases can R^2 and R^3 have?

A: Explain about the count of number of bases of ℝ2 and ℝ3.

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

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Q: different examples of application of fields

A: Groups, Rings and Fields have always eluded me. I always thought they were useful (instinctively)…

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: What are the greatest common divisors of the following pairs of integers? You can enter the exponent…

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Q: Use Modular Exponentiation method to find 5234mod 9.

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

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Q: form of (3+3i)^5

A: Given,      (3+3i)5

Q: (6.1 x 10) (4 x 1o*) Give your answer in scientific notation. SHOW YOUR WORK!! Edit Insert Format…

A: Definition used -               Product of two numbers in scientific notation -…

Q: What is the greatest negative coterminal amgle of -783 degrees?

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Q: (8.9x10-17) + (1-599×10*15) =

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

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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: Use Fermat's Theorem to verify 17 divides 11¹04 + 1.

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Q: 1745 into prime

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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: What is the remainder when 323232 is divided by 7?

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

A: jyujhjyukjhjkkhjjghfgf

Q: Using Euler’s Theorem, find the last two digits of 4444^3333

A: Let us find the last two digit of the given expression by using Euler's Theorem in the next steps.

Q: Using Extended Euclidean Theorem, determine the multiplicative Inverse of 24143 with modulo 40902.

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Q: What is 1.939 x 10 in standard form? ) A) 0.000001939 B) 0.01939 C) 19,390 D) 193,900

A: we have to write in standard form of the given expression