Find a primitive root modulo 2 * 19^2022

Q: Least residue of 8^68 modulo 17

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Q: Show that 2^645 -1 is a pseudoprime. i know 2>1 and 645 is composite. But how to prove 645 divides…

A: A pseudoprime or probable prime is actually not a prime number or it is a composite number which…

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: If x^677 ≡ 3 mod 2020, find x.

A: We have   x677≡3mod2020⇒x677-3=2020m   where m is integer different values of m we get different…

Q: Is 1501 square modulo of 3738

A: Explanation:To determine if 1501 is a square modulo 3738, we need to find an integer x such that…

Q: Determine the least residue of 56^1010 (mod 323).

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Q: Compute 17^7121 (mod 11).

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Q: Find in modulus-argument form [(1+iv3)³/ E-1+i)²]°.

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Q: Prove that 2^10 + 5^12 is a composite number.

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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: Find all solutions for x, up to congruence 7^78 (mod 79)

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Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

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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: Calculate 2^1212 (mod 9211), reducing it to a positive number less than 9211. Show your…

A: We have to find out remainder when Noted that Since So to get the required result ,we have to find…

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

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Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

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 mod of (2-4i)^1/2

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Q: prove if a and b are both odd integer, then 16/ (a^4) + (b^4) -2.

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Q: 5^14 ( mod 26).

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Q: -1

A: No it is not a prime numbers

Q: Use descent to find x,y such that x? + y? = 61 starting from 112 + 12 = 2 · 61.

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Q: Compute 59^11 mod 13 = You should know how to do this without a calculator by using the modulo…

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Q: Find 80^81 mod 11

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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: A museum wishes to display five paintings next to one another on a wall. In how many ways may this…

A: The question is based on permutations. Number of ways r things can be arranged in n spots are: nPr =…

Q: What is order of 5^15 congruent to 6547(mod20143)?

A: We want to find the order of 515 modulo 20143 given that 515≡6547 (mod 20143).

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

A: Solution

Q: 3^69 (mod 23)  6^2003 (mod 11)

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