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## Related Algebra Q&A

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

A: Solve the given problem.

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

A: Given: To show that 4(44!)+49 is divisible by 47. To explain the given statement as follows,

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: . Show that sup{3 – 2 : n = 1,2, ...} = 3. %3D

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Q: What is 5^22 congruent to? Please show steps.

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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: The great est common divisor of 0 and 5 is (1 (2

A: Since 5 divides 0 as well as 5 divides 5 Also, 5 is the greatest integer which divides 5

Q: Given any set of 15 integers, must there be two that have the same remainder when divided by 12?…

A: We have 12 remainders when a integer is divided by 12 those are 0,1,2,3,4,5,6,7,8,9,10,11 Let us…

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Q: I would like a proof to this statement, if it includes the definition of divisibility, even better.…

A: Division Algorithm: Let a and b be integers with b>0. Then there exist unique integers q and r…

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Q: Rehan proved by mathematical induction that for all the positive integers, n^3+2n is divisible by 3.…

A: Use principle of mathematical induction to prove this statement as following:-

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Q: Rehan proved by mathematical induction that for all the positive integers, n^3+2n is divisible by 3.…

A: Show true for n=1 Let P(n):=n^3+2n be the statement now 3=1+2=(1)^3+2(1) 3 is definitely divisible…

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Q: Rehan proved by mathematical induction that for all the positive integers, n^3+2n is divisible by 3.…

A: Click to see the answer

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Q: Find, If possible, A + B, A- B, 2A, 2A - B, and B +A. (If not possible, enter IMPOSSIBLE In any…

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Q: Number Theory

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Q: When to use the simpsons rule 1 3 and 3/8?

A: The simpson 1/3 rule is use when the given number of sub intervals is divisible by 2. That given…

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Q: 2. Use prove by contrapositive to show that: (For real numbers a, b, c) If (a – b)² + (b – c)² + (c-…

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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.…

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Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

A: Click to see the answer

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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 .

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Q: Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it…

A: (a)The fill up for the statement to rewrite the given statement: Is there an integer n such that n…

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Q: Is 7, 8, 9, 11 are pairwise relatively prime. صواب ihi

A: Two nos. a and b are said to be relatively prime iff gcd(a,b)=1

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Q: Prove the statement. "For any integer n, nº +4 is not divisible by 8." by Contradiction.

A: Given: n be any integer. To prove: n3+4 is not divisible by 8.

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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.

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Q: What is the contrapositive of the statement “ A rectangle R with side lengths 1 and x, where x is…

A: theory Indeed, the ratio between length and width must be rational, even if we don't require the…

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Q: Prove: (a) 2ab <a² + b²; (b) ab + ac + bc < a² + b² + c².

A: According to the given information, it is required to prove the following. For part (a)

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Q: 1, test the claim that there is no difference betv (2). needed.)

A: * Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at…

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Q: in= aRo can direetly /KT. by gomma fometion, We write Jo a Kox2 &KT 2

A: If you have any doubts in the solution please ask me in comments i will reply you as soon as…

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

A: Click to see the answer

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Q: 40fa, b, c, p, q, r are non-zero real numbers, such that a <b<c and fox)=(x-a)(x-b)(x-c)-p'(x- a)-…

A: Observe if x3+ax2+bx+c is some general monic cubic polynomial with roots α, β, γ, then,…

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Q: rix with even mumber of permuta Q4. If all elements of A and A are integer numbers, what are the…

A: Let A be any n×n Matrix with integer entries

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Q: Evaluate projba if a = (13, 5, 1) and b= (2, 1, –1). %3D

A: Given, To determine

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Q: Show that there are no prime triples other than 3, 5, 7.

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Q: Prove 3 2 (w)

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Q: What is 13√3/26 in simplest form?

A: The solution is :

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Q: A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the…

A: Given: A (3 × 7) rectangle divided into 21 squares each with red or black colour. The area of the…

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Q: A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the…

A: Solution: let suppose the board is a 3 × 7 rectangle.

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Q: A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the…

A: Given that, A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black.…

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A: Solution..

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Q: Prove the “rule of 9”: an integer is divisible by 9 if and only if the sum of its digits is…

A: See the attachment

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Q: Prove by contrapositive that if 7x+9 is even , then x is odd

A: Prove by contrapositive that if 7x+9 is even then'x' is odd = proof by contrapositive suppise 'x' is…

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

A: Click to see the answer

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Q: Prove or disprove: 2 + 8 + 18 + ... + 2n^2 = n^2 + n

A: Please see the explanation below

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

A: Types of integers : Odd integers : The integer which is not divided by 2 . It has the form 2k+1…

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Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n>-3

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Q: Which pairs of the integers -11, -8, -7, -1, 0, 3, and 17 are congruent modulo 7?

A: -11≡3 (mod 7) holds Since -11-3 = -14 is divisible by 7 and leaves remainder 0. -7≡ 0 (mod 7)…

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Q: A natural number greater than 1 that has only itself and 1 as factors is called a/an number.

A: Given that A natural number greater than 1 that has only itself and 1 as factors is called…

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Q: Consider the statement: "there are no integers and such that 20a+4b%3D1." Is this true or false?…

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Q: A palindrome is a number that reads the same forward and backward, such as 2,743,472. (a) Give a…

A: Solve the following