Question 3. of 24. Show that if n is an odd integer, then n³ - nis multiple

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: Simply the expression to a sum of 2 terms and then factor the result to obtain the product of sums:…

A: The complete solution is in given below

Q: How many 10 digit real even number can be created (It cannot start with a 0) with 5 zeroes and 5…

A: Basic concepts of making combination are used. Information given, As we have only two choices of…

Q: Consider the following statement. 9n<5^n   What is the smallest positive integer n for which the…

A:

Q: 2 +3" En=D0 %3D 5n+1 Select one: O True O False 5/56

A:

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: 4. Knowing that 1 + 3 + 5 + …+ (2n – 1) = n², find 1++3 +5 + .…+ 135 =

A: Solution :   Given that  1 + 3 + 5 + ... + (2n - 1) = n2    -----(1)

Q: Show that 3+ V5 is irational number

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Q: Prove the following using either direct proof, indirect proof, or proof by contradiction. 1. If n…

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Q: 2n 10. Prove that 31 (5 - 1) for every integer n 2 0.

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Q: Prove that the statement is true for every positive integer n.

A: We know that the sum of a geometric series of the form: a+ar+ar2+ar3+...........+arn-1 with the…

Q: Part III: Prove the following 5. Prove that 32.753215321... is a rational number.

A:

Q: 5) Let n be a positive integer such that 7 | (8-1). Prove that 7 | (8=*1 - 1). (Hint: Rewrite 8*1…

A: Given: Let n be a positive integer such that 78n-1. To prove: 78n+1-1

Q: For how many positive integers 'n', n3-8n2 + 20n - 13 is a prime?

A: Introduction :

Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.

A: Answer

Q: X sin (7) 4 n=1 راح n

A: We have to check the convergence of the series  ∑n=1∞sin(πn4)n2

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT How many positive integers n ≤ 1000 are coprime with N=90

A: We know that 90=2×32×5 Numbers less than 1000 which are divisible by 2 =10002=500 Numbers less than…

Q: 5. Prove that n² is an even number if and only if 3n + 1 is an odd number by proving a) If n² is…

A: To Prove: We have to prove that n2 is an even number if and only if 3n+1 is an odd number.

Q: Using direct proof method, prove the following. If n is an even integer then n2 + 13 is odd.

A: Direct proof

Q: Determine the following. 1. AnB 2. AUB 3. |A|

A:

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

A: Answer)

Q: Show that 2 + V5 is irational number

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Q: You are provided with 15 and 20 cent notes. Show using strong induc- tion that all amount that are…

A: Given: Let us consider based on the given data that Sk = 5k and be S1 = 5. Because given that all…

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: Find the ones 171 22 digit of n=11 +3 +|

A: We need to determine the ones digit of the expression: 11171+322+1. We need to determine the ones…

Q: 1. Show that 2465 is a Carmichael number.

A: Let n=2465

Q: prove the following using either direct or indirect proof  a. if a is an odd integer, then…

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Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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Q: Q3. (a) Consider the continuous function f(t)=sin(27nt). i) What is the period of f(t)? ii) What is…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…