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

Q: Prove that 2n32n - 1 is always divisible by 17.

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Q: show that if x is an integer then x2+x-41= 0 produce prime numbers

A: Here show that if x is an integer then  produce prime numbers.

Q: 2. Prove that 11" – 7" is divisible by 4 for any positive integer п.

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Q: Prove that for all natural number n, 52n-1 is divisible by 8.

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Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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Q: Use a direct proof to show that the product of two odd integers is odd.

A: Introduction: A direct proof is a series of statements, the final of which is the conclusion to be…

Q: 4. Describe all zero-divisors and units of Z6 O ZOQ

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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: Show that every positive integer can be written as the product of a square (possibly 1) and a…

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Q: How can I prove by induction that 2^n + 1 is divisible by three for all odd integers

A: To apply mathematical induction to show that 2^n+1 is divisible by 3 if n is odd

Q: divisible by 3 for

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Q: Suppose 48 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

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Q: How many positive integers between 5 and 31 (a) are divisible by 3? (b) are divisible by 4? (C) are…

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Q: Suppose 50 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

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Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

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Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: If n = p,P2 ... P where the p, are distinct prime numbers, how many ways can n be written as a…

A: First let us formulate the problem in a different way. Look! we have to find the total number of…

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

A: Consider the provided expression,

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: show that if x is an integer then x^2+x-41= 0 produce prime numbers

A: This question is taken from the quadratic equation in which we have to find the roots of the given…

Q: Use indirect proof to show that if n is an integer and n^3 + 5 is odd, then n is even.

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Q: what are ALL the six-digit numbers of the form 47_8_6 that are divisible by 24?

A: The six-digit number has form 47__8__6

Q: Suppose 59 cars start at a car race. In how many ways can the top 3 cars finish the race? ... The…

A: There is total 59 cars.

Q: How many integer solutions to x1 + x2 + x3 + x4 = 32 are there for which x1≥6, x2 ≥5, x3 ≥3 and x4…

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Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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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: SHOW THAT 3^2N - 1 IS DIVISIBLE BY 8 FOR ALL POSITIVE INTEGERS.

A: We prove this by induction.

Q: Prove that 9? −1 is divisible by 8,for all n ≥ 1

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Q: Develop a simple expression for the entries of A", where n is a positive integer and 1 A = -IN -IN

A: To get a simple expression for the entries of An, where n is a positive integer. A=112012

Q: The positive integers that are divisors of 68 are

A: We will use multiple method to find all the divisor of the given number .

Q: 2. Show that 1184 – 534 is divisible by 7. -

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Q: How many integer solutions to x1+ x2+ x3+ x4 = 36 are there for which æ1 > 5, x2 > 3, x3 > 5 and æ4…

A: We have to find the number of solutions to x1+x2+x3+x4=36 for which x1≥5, x2≥3, x3≥5 & x4≥6.

Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

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Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

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

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Q: (c) Prove that n? + 1 is not divisible by 3 for every integer п.

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Q: If A #8 then

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Q: Find all positive integers n for which n1º +1 is divisible by 10.

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Q: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

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Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

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Q: 1. Use Direct Proof to prove that the product of two consecutive integers is divisible by 2.

A: We have to prove that product of two consecutive integers is divisible by 2.

Q: Show that every odd integer is the difference between two consecutive perfect squares.

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Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

Q: Show by induction that 21" – 8" is divisible by 13 for all n> 0

A: For the solution follow the next steps.

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: Show by induction that 19" – 8" is divisible by 11 for all n >0

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Q: divisible

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.