Are there a way where I can turn 6d = k(k^2 + 5) to 6 ( an integer ) = k+1 ((k+1)^2 + 5)? 15)for eachn(n*+5) is divisible by ointegerProof (ay induction)PO)= "o (0?+5) is divisible by 6"? 610 =0 since6.0 = 0 VP(x) > P(Kti): Let KE ə k20AssumePCK) is true"K (K?+5) is divisible bythat is,So this.mean that6d = k(K?+5) for somedefinitionof divisi bility.intoger d.byNTS: kti((K+)*+5) is divisible by 661 KHI ((K+i)?+5)d= ktH ((K+)45)%3DNow,od = K(K?+5),)

Answered: Image /qna-images/answer/039d366d-a888-4784-b9a6-526cb9df3b79.jpg

Answered: 15) n(n*+5) is divisible by for each…

Math

Advanced Math

15) n(n*+5) is divisible by for each integer

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.5: Mathematical Induction

Problem 27E

See similar textbooks

Related questions

Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: Suppose you draw n lines in the plane so that every pair of lines cross (no lines are parallel) and…

A: Let n be the number of non parallel lines. Given that number of regions= Rn Let Un represent maximum…

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

Q: The number 0.60 is rational and can be represented in finitely many digits in decimal a. can it be…

A: Questions regarding the binary representation of 0.6

Q: Find all three-digit numbers with different digits with the property that those numbers are…

A: Given that it is to be found all three-digit numbers with different digits with the property that…

Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: Let x be the required number. The number is divisible by 3, so it leaves the remainder 0 when it is…

Q: Use the the Binomial Theorem to calculate 11^11 (just giving the end result is not enough.)

A: To find the value of 1111 using the binomial theorem. Now, the Binomial expansion of (1+x)n is:…

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: What is the exponent on the x variable of the 3st/nd/rd/th term in the expansion of 17 (x2 +3y)" ?…

A: using formula:-

Q: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: 3. Use your result above to show that the number 1,111,111,113 is divisible by 3 while the number…

Q: Give a combinatorial interpretation of the coefficientof x4 in the expansion (1 + x + x2 + x3 +⋯)3.…

Q: Suppose each license plate in a certain state has three letters followed by three digits. The…

A: * License plate must have 3 letters and 3 digits ; repetitions allowed.Also , letters H and L…

Q: Suppose 51 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

A: Solution: From the given information, number of cars start at a car race is 51.

Q: divisible by 3 for

Q: Which term of the expansion of (x° + 7) contains x 28 ,36 Term number contains æ36

Q: Which positive integers less than 20 are relatively prime to 20?

Q: Let n be a number with 3 digits. (i.e 100sns 999) Show that if the sum of digits of n is divisible…

Q: Prove that 2^10 + 5^12 is a composite number.

Q: Explain how to expand (a + b)' using the binomial theorem n an-kbk. Be specific. k expression, k-0

A: Given: a+b7 The binomial theorem: a+bN=∑n=0NNnaN-nbn where Nn=N!n!N-n!

Q: Find: The sum of all positive integers less than 400 which are not divisible by 5.

Q: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: How to find the last two ditgits of 2^2021 ?

A: Solve the given problem.

Q: A positive integer n is called superperfect if ơ(ơ(n) = 2n Show that 16 is superperfect.

Q: how to prove √6 is irrational

Q: 5. Give a recursive definition of the set of positive integers that are multiples of 5.

A: Solution

Q: what are the first three terms in the binamial, expansion of (2a-0,5b) 1.

A: Given

Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that every integer greater than 11 is the sum of two composite integers.

Q: Integers with different values in each digit can be expanded in a similar way. For these integers,…

A: Let we have a number 5267843 This number can be expanded as…

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

A: We prove this by induction.

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: 5. Find the number of positive integers less than 700 that are divisible by 3 but not divisible by…

Q: Which numbers in Z17 are relatively prime to 17? Enter your answer as a comma separated list of…

A: The objective of the question is determine all al relatively prime to 17 in Z17 .

Q: The sum of all positive integers less than 400 which are divisible by 5.

A: Positive integers less than 400 which are divisible by 5 are⇒n=79 5,10,15,20,...,395 The above…

Q: 4. Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can…

A: We have to find the sum of all divisor of 5020 and then the amicable pair of the number.

Q: Suppose 26 cars start at a car race. In how many ways can the top 3 cars finish the race? ..... The…

Q: Determine all natural numbers divisible by 8 whose sum of digits is less than 10 and the product of…

A: Permutation and combination concepts will be used to filter out all the 3 scenarios in getting…

Q: is there integer that has reminder of 2 when its devided by 5?

A: There are infinite number of integers that has reminder of 2 when its divided by 5

Q: Explain how to expand (a + b)7 using the binomial theorem expression, a"-kb. Be specific.

Q: The sum of any two integers of the from 4k + 1 is always: Even O prime Zero Odd

A: If a number n is not divisible by 2 then it is an odd number. If a number n divisible by 2 then it…

Q: Use binomial theorum to expand (1 + 1/x)^7

Q: 3. There are seven students who always compare their CS test grades. They discovered that either the…

A: It is given that there are seven students who always compare their CS test grades. They discovered…

Q: (5 × 104)(8 × 105) 4 × 106 (10 × 10−5)(9 × 106) 5 × 109

A: We have to calculate the values in scientific form of And

Q: 5!, called 5_______ , is the product of all positive integers from_________ down through________ .…

A: For any positive integer n, n! is the product of all the positive integers from 1 to n. That is,…

Q: How many natural number that are less or equal to 1000 and that are not multiplea of 3,5or7 exist

A: To find: Number of natural numbers ≤1000 that are not multiple of 3 or 5 or 7.

Q: how did they get 9x^2 from (x^4)/(5x^2)mod11 ?

A: Use of z11[x],

Q: What are integers and how can it be easy for me to use them?

A: An integer is a whole number (not a fraction) that can be positive, negative, or zero. Therefore,…

Question

Are there a way where I can turn 6d = k(k^2 + 5) to 6 ( an integer ) = k+1 ((k+1)^2 + 5)?

15)
for each
n(n*+5) is divisible by o
integer
Proof (ay induction)
PO)= "o (0?+5) is divisible by 6"? 610 =0 since
6.0 = 0 V
P(x) > P(Kti): Let KE ə k20
Assume
PCK) is true
"K (K?+5) is divisible by
that is,
So this.mean that
6d = k(K?+5) for some
definition
of divisi bility.
intoger d.by
NTS: kti((K+)*+5) is divisible by 6
61 KHI ((K+i)?+5)d= ktH ((K+)45)
%3D
Now,
od = K(K?+5),)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here