Proof that (11^n) −6 is divisible by 5 for all values of n ≥1

Reduce (25)^(25)^(32) mod 23 to smallest positive number.

Let P(n) be the statement “the number 2^2n -1 is divisible by 3”. Use mathematicalinduction to show that P(n) is true for all n >0

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Question 44 ddd Computer Science Prove that log(n!) = Θ(n log n). (Logarithms are based 2)

The code for Algorithm computeSpan2(P):Input: An n-element array P of numbersOutput: An n-element array S of numbers such that S[i] is the span of the stock on day i.

TRUE OR FALSE N Queens' problem can be effectively solved using dynamic programming.

Find the greatest common divisor (GCD) of 36 and 54 using the Euclidean algorithm. Show your work.

Show that 5n+5 is O(n). (pick c and n0)

University of Bahrain Department of Computer Science ITCS254 Discrete Structure I First Semester 2022/2023 Homework 4 (1) show that 21 divides 4+1 +52n-1 for n ≥ 1 (2) Prove by Induction n ≥ 3 that : n Σ(r− 1)² = = r=1 (3) Let T₁ = 1, Tn = 3Tn-1 + 4 for n ≥ 2. Show that Tn = 3" - 2 for n ≥ 1 3 +