Show that 4(44!) + 49 is divisib by 47

Q: (1) What is gcd(31212021 + 3, 31212021 - 3)? I am aware of 3121 is a prime number, and 2021 is…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

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

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Q: Show that √2 + √3 is irrational.

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Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate ?(x)

A: given , expression :- 32x+7 we have to prove that given expression is divisible by 4 .

Q: What is the coefficeint of a²b³cª in the expansion of (a + 2b + 3c)® ?

A: In the given question we have to find the coefficient of  a2b3c4 in expansion of a+2b+3c9

Q: o use divisibility in this problem but i am not sure where to start. Prove or disprove (with a…

A: Introduction: If a and b are integers, a divides b if c is an integer and ac = b. The symbol a|b…

Q: 6. A. Show that 81 – x²dx : 81n %3| 4

A: According to company rule we can answer only first question and rest can be reposted

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate P(x)

A: Yes we can use mathematical induction for Natural number x.

Q: The easiest way to evaluate 2 8 5 -4 3 5 7 0 is to expand about the elements in -6

A: A square matrix is a matrix whose number of rows and columns is the same. Determinant can be…

Q: 1) Use the chain rulc to find the deriva five of fcx) = 4(-3x6+7x5)7 You do not necd to expand…

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

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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: 9.) Is 9" + 3 is divisible by 4? PROVE IT!

A: Given : 9n+3 is divisible by 4. To Prove: The given statement is true for n=k+1. Consider Tn=9n+3.…

Q: divisible by 3 for

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Q: Show that (n + 1)!)" < 2! · 4! - (2n)!.

A: The objective is to prove the given statement using induction

Q: In Z6, show that 4 | 2; in Z8, show that 3 | 7; in Z15, show that 9 | 12.

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Q: Show by mathematical l Induction y 4n-2 3. +17 can be divided by +22 possitive integers 16 far all

A: To prove the given statement by using mathematical induction.

Q: What's is 38392% of 4

A: Given,  38392% of 4   We have to calculate it.

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: Prove that 3:8 is equivalent to 12:32

A: According to the question, we have to prove that the ratio 3:8 is equivalent to 12:32. A ratio is a…

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

A: Solve the given problem.

Q: If the product of two integers is 2'3*5?7!" and their great- est common divisor is 2°345, what is…

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Q: ken two at a ken three at a

A: 1 2 3 4 5 6 j o y f u l The different arrangements formed from the 6 letters word = 6!

Q: 4. Prove by contradiction: VmeZ, 7m+4 is not divisible by 7

A: Contrary suppose that,   m is an integer such that 7 m+4 is divisible by 7. By using the definition…

Q: Prove 3√3  is irrational

A: See the attachment.

Q: 1. Simplify the expresslon below. @3x ®. x12 ©3x12. . . n... O x64

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the coefficient of z12 in (6-12z)12 O a. P(12,6)* -612 O b. C(12,0)* -(1212) O . 1212 O d.…

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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: what is 6squared + 7

A: It is given that 6 squared + 7.

Q: 8. Show that 4 29! +5! is divisible by 31.

A: We have to prove that 4.29!+5! is divisible by 31.

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: Number Theory

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

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Q: Show that if 2n−1 is prime then n is prime.

A: We have to show that if 2n-1 is prime then n is prime.

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

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Q: What is (3a- 82² – 10a – 24) ( – 4)? O 3a2 + 4x + 3+ エー4 4 O 3x? + 4x + 6 O 3x? + 4x + 3- -4 O 322…

A:

Q: If  n×k divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is…

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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: Compute  7!/3!(7-3)!

A: Obtain the value of 7!/3!(7-3)!:

Q: Prove that if 3|n^2 then 3|n using contraposition and cases

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Q: 4503 is divisible by 2,3,,5,6,9or 10

A: 4503 is divisible by 2, 3, 5, 6, 9 or 10.

Q: nd [Po90].

A: answer is in next step

Q: How many terms are there in the expansion of (a+4b)^20 ?

A: Given expression, (a+4b)20

Q: What does the divisibility rule of 4 and 8 have in common ?

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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: If X is a positive integer divisible by 6, and X <60 What is the greatcst possibe vaive of X 7

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Q: :Compute the product. 2 -35 2 -2 4 1 0 -1 4 9 -1 -3 -41 ? ?

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Q: Prove that n(n + 1)(n + 2) is always divisible by 6

A: