Find all the primes less than 50 with primitive root 3.

Q: 2. By using Fermat's Theorem, solve, 21x = 12(mod 17).

A: First, we simplify the equation by reducing the coefficients modulo 17. This is because in modular…

Q: Prove by induction, '2 divides n2+n whenever n is a positive intege

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Q: Show that there is a prime number p such that p+4 and p+6 are also prime numbers.

A: Prime number is a number p having only two divisors p and 1 only.

Q: 6. Prove that 2n +5 and 3n+7 are relatively prime for every integer n.

A: What is Relatively Prime Numbers: Relatively prime or coprime numbers are two such numbers which…

Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

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Q: O Determine whether M₁1 = 2¹¹ – 1 is prime by checking primes less than √M₁.

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Q: 10. Find all primes p such that 29p+1 is a square.

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Q: Find the six smallest even perfect numbers.

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Q: Find all primes of the form 22" + 5, where n is a nonnegative integer.

A: Answer)

Q: Compute the prime factorization of:         gcd(699840, 1215000)            699840 = 26 · 37 · 5…

A: We have to find the prime factorization of gcd of two given numbers.

Q: show that no integer of the form n^3+1 is a prime other than 2

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Q: Prove that the number in between twin primes is always a multiple of 6.

A: A Twin prime are those numbers which are prime and having a difference of two ( 2 ) between the two…

Q: show that for every positive integer n there is a prime whose decimal expansion contains n…

A: so we have to prove , for every positive integer n there is a prime whose decimal expansion contains…