Question

In: Advanced Math

Let ?=2^(2^?)+1 be a prime that n>1 1. Show that ? ≡ 2(mod5) 2. Prove that...

Let ?=2^(2^?)+1 be a prime that n>1

1. Show that ? ≡ 2(mod5)

2. Prove that 5 is a primitive root modulo ?

Solutions

Expert Solution


Related Solutions

If n>=2, prove the number of prime factors of n is less than 2ln n.
If n>=2, prove the number of prime factors of n is less than 2ln n.
Using the pumping lemma, prove that the language {1^n | n is a prime number} is...
Using the pumping lemma, prove that the language {1^n | n is a prime number} is not regular.
Let f1 = 1 and f2=1 and for all n>2 Let fn = fn-1+fn-2. Prove that...
Let f1 = 1 and f2=1 and for all n>2 Let fn = fn-1+fn-2. Prove that for all n, there is no prime p that divides noth fn and fn+1
Let x1 > 1 and xn+1 := 2−1/xn for n ∈ N. Show that xn is...
Let x1 > 1 and xn+1 := 2−1/xn for n ∈ N. Show that xn is bounded and monotone. Find the limit. Prove by induction
Let p be an integer other than 0, ±1. (a) Prove that p is prime if...
Let p be an integer other than 0, ±1. (a) Prove that p is prime if and only if it has the property that whenever r and s are integers such that p = rs, then either r = ±1 or s = ±1. (b) Prove that p is prime if and only if it has the property that whenever b and c are integers such that p | bc, then either p | b or p | c.
i need a very detailed proof (Show your work!) Let n > 1. Prove: The sum...
i need a very detailed proof (Show your work!) Let n > 1. Prove: The sum of the positive integers less than or equal to n is a divisor of the product of the positive integers less than or equal to n if and only if n + 1 is composite.   
let n belongs to N and let a, b belong to Z. prove that a is...
let n belongs to N and let a, b belong to Z. prove that a is congruent to b, mod n, if and only if a and b have the same remainder when divided by n.
Let p be an odd prime. (a) (*) Prove that there is a primitive root modulo...
Let p be an odd prime. (a) (*) Prove that there is a primitive root modulo p2 . (Hint: Use that if a, b have orders n, m, with gcd(n, m) = 1, then ab has order nm.) (b) Prove that for any n, there is a primitive root modulo pn. (c) Explicitly find a primitive root modulo 125. Please do all parts. Thank you in advance
1.)Prove that f(n) = O(g(n)), given: F(n) = 2n + 10; g(n) = n 2.)Show that...
1.)Prove that f(n) = O(g(n)), given: F(n) = 2n + 10; g(n) = n 2.)Show that 5n2 – 15n + 100 is Θ(n2 ) 3.)Is 5n2 O(n)?
Let gcd(a, p) = 1 with p a prime. Show that if a has at least...
Let gcd(a, p) = 1 with p a prime. Show that if a has at least one square root, then a has exactly 2 roots. [hint: look at generators or use x^2 = y^2 (mod p) and use the fact that ab = 0 (mod p) the one of a or b must be 0(why?) ]
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT