Show that n22-1 is division by 8, if n is an odd positive integer

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: Every positive integer has a prime division

A: The Fundamental theorem of arithmetic (also called the unique factorization theorem) is a theorem…

Q: 2. 6n - 1 is divisible by 5 for n any positive integer

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Q: Show that 3 · 4n + 51 is divisible by 3 and 9 for all positive integers n.

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Q: What is the degree of each term in the expansion of (x+5y)^21 ?

A: The dree of the term is the sum of the powers of the variable.  Note that the binomial expansion of…

Q: 2.269910988417 x 10^23 so what will i use to bring it down to under 100 ? how to divide it ?

A: so to bring it down 100 we just divide it by number x we now have to find the value of x

Q: Prove that 5 does not divide 5n+3 for any integer n.

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Q: 4. Find the 11th term in the expansion of 25 3r- + 5.x

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Q: What are the coefficients of æ5000 and æ4999 in the simplified expansion of (5æª – 2)²2021?

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Q: show that n(n^2-1)(n+2) is divisible by 4 for all integers n

A: To show that n(n^2-1)(n+2) is divisible by 4 for all integers n

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: Without performing the divisions, determine whether the integers 176521221 and 149235678 are…

A: (4) Given integers are 176521221 and 149235678. We have to check whether the integers 176521221 and…

Q: 3. Suppose that a, b and c are positive integers with 2"365c = 36000. What is the value of 3a + 4b…

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Q: The term involving x^9 in the expansion of (x2 + 2/x)12 is

A: We are asked to fine the term that involving x^9

Q: Suppose n ≥ 2 is an integer with the property that whenever a prime p divides n, p 2 also divides n…

A: let n=p1a1p2a2....pmam be the prime factorization of n  Here p1,p2....pm are all distinct primes and…

Q: 6. Find the remainder of 17036543 on division by 25.

A: Thus, remainder = 2

Q: Prove by cases that n2−1 is divisible by 3 when n is an integer not divisible by 3.

A: The detailed solution is given below Thank you

Q: Find the term that contains x^8 in the expansion of (3x-1)^11

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Q: Show that n2-1 is division by 8, if n is an odd positive integer

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Q: Find the smallest integer n for which the property below hold 3n > 2967 n =

A: Given query is to find the value of n.

Q: Solve for x using The Division Algorithim : 937 =x (mod 4)

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Q: Multiply three consecutive integers together and then add the second integer to that product. Use…

A: Consider three consecutive numbers x, (x+1), (x+2). Take a product of these numbers we get,…

Q: use the Euclid's division lemma to show that the cube if any positive integer is either of the from…

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Q: Find an expression, in terms of n for the coefficient of x in the expansion (1+4x) + (1+4x)² +…

A: ANSWER :

Q: Prove that 6-1 is divisible by 5 for any n 21.

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Q: 3. Show that 13" – 7ª is divisible by 6 for n > 1.

A: As per Bartleby guidelines we can solve any one question at a time. Hope you understand.

Q: If in the expansion of (1 + n}+", the 5th term is 24 times the 3rd term, fnd the value of n.

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Q: 4. Find the 11th term in the expansion of 25 3x + 5xi

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Q: find the fourth term in the expansion of  (x +  1   9…

A: Recall the fact that the general term of expansion ( a + b )n is as follows.

Q: If n = 4k + 3, does 8 divide n2 - 1? (Assume that n and k represent integers.) O Yes, because n2 - 1…

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Q: Find the 3rd term in the expansion of (5x 2)4 in simplest form.

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Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers

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Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers n.

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Q: Use the quotient remainder theorem and division into cases to show for all integers n, the integer…

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Q: Answer the following. 1. Find x if 2x309 is divisible by 9 2 Find the canonical prime factorization…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Al. a. Find an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is…

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Q: Prove 8 divides 34h+1+52h+1 whenever h is a positive integer

A: We need to prove that 8 divides 34h+1+52h+1 whenever h is a positive integer by Mathematical…

Q: Prove that 3" + 1 is divisible by 4 whenever n is an odd positive integer.

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Q: If n is an even integer, then 3n° is an even integer.

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Q: Show for all integers n2 0 that 91 (4" - 1). a.

A: A. We will solve the question using the method of mathematical induction.

Q: 8. Show that no prime number of the form 4k +3 can divide a number of the form n2 + 1.

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Q: Show that n22-1 is division by 8, if n is an odd positive integer

A: If n is a odd positive integer n can be written as   n = 2k+1 by substituting in n2-1 n2-1 =…

Q: Find a factor of the following integer. 2289 - 1

A: We have to factor

Q: Obtain the expansion of : 2 up to the term in x8 1-3x2

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Q: Is it true that for any odd n the number 2" +1 is divisible by 3? Prove your answer.

A: We prove this by using PMI(Principle of Mathematical induction)

Q: find the simple formula for the product (1-1/2)(1-1/3)...(1-1/n)

A: topic - product of series  answer is 1/n

Q: 2 ) + ("**) = n²- .2 2

A: