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

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

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

A:

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

A: Answer)

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

A:

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…