prove that is 11^k-4^k is divisible by 7    use mathematical induction

Q: Write a complete residue system modulo 13 consisting only of odd integers.

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Q: Use mathematical induction to show that 5? − 1 is divisible by 4. Determine the starting value as…

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Q: Establish by mathematical induction that any postage of at least 12c can be obtained using 3c and 7c…

A: We have to establish by mathematical induction that any postage of at least 12c can be obtainedusing…

Q: Show that the sum of all  odd  integers between 1 and 1000 which are divisible by 3 is 83667

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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: 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: Show that there are infinitely many primes of the form 4k + 3.

A: We have to show that there are  infinitely many primes of the form 4k+3.

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: Prove by mathematical induction

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Prove that 279,930 is divisible by 7 using Fermat's Little Theorem.

A: We have to prove that 279930 is divisible by 7 using Fermat's Little theorem. The Fermat's little…

Q: Prove that for all integers, n , n^3-n is divisible by 3.

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Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: V nEN, 7"- 3n is a multiple of 4.

A: We have to find   For all n= natural number we have to

Q: Use the definition of an r-permutation, or the product rule to de number of trifectas possible in a…

A: Given: To explain the given statement as follows:

Q: Prove that peanos 5th axiom and principal of mathematical induction are equivalent

A: We have to show that Peano's 5th axiom and principal of mathematical induction are equivalent.

Q: Expand in binomial theorem (2x-y)7

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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: 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: What is the least residue of 7162 modulo 17?

A: Multiplication rule for congruencesIf a ≡ b (mod n) and c ≡ d (mod n), thenac ≡ bd (mod n). Power…

Q: Use generating functions to determine the number of differentways 15 identical stuffed animals can…

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Q: Find the least residue of  -5 -46 modulo 14.

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Q: How many 5-digit even numbers can be formed using the digits 2, 4, 6, 7, 9 if no repetition is…

A: Given:

Q: Compute the sum of all integers between 60 and 150 that are exactly divisible by 8.

A: Consider the given range of number 60 to 150

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: Prove through mathematical induction that...

A: Mathematical induction is a method of proving a statement, formula, or expression. In this, the…

Q: Suppose that n is an integer such that n≥3. Using a combinatorial proof, show that:

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Q: What sequence of pseudorandom numbers is generated using the pure multiplicative generator xn+1 =…

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Q: a) Proe by induction on n3, that 23"-/ is diwisible bu

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Q: or an integer n>=3, an n-gon is an n-sided polygon. (example, a 3-gon is a triangle, 4-gon is a…

A: To prove: the sum of the interior anles of every polygon with n sides is n-2180° Now we shall take a…

Q: Prove that AXB|=A²B² - (AB)².

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Q: 6. Establish by mathematical induction that any postage of at least 12¢ can be obtained using 3¢ and…

A: 12¢=4×3¢+0×7¢13¢=2×3¢+1×7¢14¢=0×3¢+2×7¢15¢=5×3¢+0×7¢16¢=3×3¢+1×7¢17¢=1×3¢+2×7¢…

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: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: 2. Prove that the Cartesian product N Nis countable

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Q: Sort this permutation [5 213 4] into identity permutation [123 4 5]. Check what's the number number…

A: The permutation is nothing but the arrangement of objects in different orders. If we permute a set…

Q: 7. What is the second step In proving by mathematical induction that for every positive Integer n,…

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Q: How many ways are there in which 2 purple stones, 1 yellow stone, 2 orange stones, and 2 red stones…

A: Given condition  :  No two stones are in the same row and no two stones are in the same column…

Q: Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 X 2 tile with…

A: Given: We have given a 2n×2n board and we want to fit the board with L-shaped tiles such that ∃ an…

Q: divisible by 3

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Q: Give a recursive definition for the set of all the positive integers that are less than 100 and not…

A: Given: Set of all positive integers that are less than 100. To find: Recursive definition for the…

Q: Use Chinese theorem to find all positive integers that makes this congruence true:        x = 2 mod…

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Q: Prove that the First Principle of Mathematical Induction is a consequenceof the Well Ordering…

A: Well ordering principle: Every non-empty set of positive integers contains a least element. In other…

Q: Find the average of the first 50 natural numbers is……………….

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Q: (2) Explain why the rational numbers are those having periodic representation or with- out infinite…

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Q: 6. Show that Autoq(Q[3], 5]) is finite.

A: To show: Autℚℚ35,53 is finite.

Q: Give an example of a pair of numbers that can be used to generate modulo residues to represent the…

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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: Use Fermat’s little theorem to find the least residue of 863 modulo 31.

A: Fermat's little theorem says: ap≡p(mod p)gcd(a,p)=1

Q: 15 of 20 -722 –8x =? limz→00 3–72²+6x+6 O Does not exist O 00 O 7

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