29. Decide whether each of these integers is congruent to 5 modulo 17. а) 80 с) —29 b) 103 d) –122

Q: 4. Write as a single power first, if possible, and then evaluate. a) 5³ x 5 b) 4⁹ ÷ 47 c) (2¹)² -5 •…

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Q: 1): For which values of n is n div 5 = -6? A): n = -30, -29, -28, -27, and -26. B): n = -30, -15,…

A: see below the answer and explanation

Q: 16. Given an odd integer a, establish that a² + (a + 2)²+(a + 4)² + 1 is divisible by 12.

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Q: 10. How many positive integers between 100 and 999 inclusive a) are divisible by 7? b) are not…

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Q: Compute C7,2. (Enter an exact number.)

A: A combination is a selection of all or part of a set of objects, without follow any order in which…

Q: Any integer of the form 12k + 11 is also of the form а) Зт + 1 b) 5m + 2 4m + 3 бт + 1

A: We have to do proper manipulation.

Q: Prove by contraposition the following theorem For integers: if n = 2 m, then n² = 4 m² (i.e., if a…

A: Introduction: Numbers divisible by 4 are those that have zeros or multiples of 4 as the last two…

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that are…

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is…

A: There are total 7 digits, such that, 2, 3, 4, 5, 6, 7 and 8.

Q: - Decide whether each of these integers is congruent to 3 modulo 7. а) 37 b) 66 d) -67 c) -17

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Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4.

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Q: The value for (91² mod32) mod17 is? a) 5 b) 3 c) 2 d) 6

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Q: Prove that Leonardo's congruous numbers are always divisible by 24.

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Q: modulo 5   B).  Evaluate 31mod5

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Q: 5. Let p = 61. Find all incongruent elements modulo 61, that have order: (а) 5 (b) 10 (с) 60

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Q: 3. a. Find the value of 0(78).

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

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

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Q: 1. For all positive integer n, which of the following expression is divisible by 6? A) 7" – 1 C) 5"…

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Q: Q1) Write the following in scientific notation 1) 1.234 10 2.) -8.765*10402 3) 105 4.) -1025

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Q: Determine whether the integer is prime or composite a.) 97^2 + 8 b.) 433

A: Topic = Algebra

Q: 7. Show that for every natural number n2 1, the integer ) + () +*(;) + - +) +22 +... +2" is…

A: Using binomial theorem:  n0+2n1+22n2....2nnn=n01n·20+n11n-1·21+n21n-2·22....nn1n-n·2n…

Q: 8) Find 7(16750440) and o(16750440)

A: We know  that,Given a positive ineger n,let Tn denote the number of positive  divisors of  n.and  σn…

Q: 10. If x and y are integers, then 4x + 12y + 3 can't be divisible by 05 O 15 08 O 33

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Q: Compute C7,2. (Enter an exact number.)

A: Obtain the value of C7,2. The value of C7,2 is obtained below:   Combination: A combination is a…

Q: In Exercises 27-46, solve the rational inequality. x+2 27. x-1 x-4 28. 2x +1 x- 4 29. x-3 4x² – 9…

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Q: (m")(2*)(m)(m³) (m')(2) Simplify and then evaluate for m = 3 and n= 7. %3D O a) (m*)(2?) = 3969 %3D…

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Q: The value for (91² mod32) mod17 is? a) 5 b) 3 c) 2 d) 6

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Q: Determine which positive integers ? have a. Exactly 2 positive divisors b. Exactly 4 positive…

A: A positive integer has exactly 2 positive divisors if and only if it is a prime number.

Q: Show that if n is an integer and n³ + 5 is odd, then n is even using a) a proof by contraposition.…

A: Proof by contradiction and contraposition

Q: Q3) b) In how many distinguishable ways can letters of the word "TENNESSEE" be ?arranged

A: Given letter is TENNESSEE Total number of letters = 9 e has occurred 4 times n has occurred 2 times…

Q: 3.) Which positive integers have an odd number of positive divisors?

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Q: 1a) Write 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 in the form „P. 1b) Express 21C, as a sum of…

A: Here AS PER POLICY I HAVE CALCULATED 3 SUBPARTS PLZ REPOST FOR REMAINING PARTS  HERE USE…

Q: Q2) In how many distinguishable ways can letters of the word ?[TENNESSEE] be arranged 12051 O 10215…

A: Explanation: Here given the 9 letters and  how many ways arranged and choose one option  In step2…

Q: Let S be the set of numbers of the form { ((-1)^(n + 1)) (n - 1)/(n + 1) } where n is an element of…

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Q: - Find A" if n is a positive integer and 3 -1 -1 2 -1 1 3 ||

A: ANSWER:

Q: 2. For all positive integer n, the expression n -n+ 3 is always divisible by A) 6 only B) 2 and 3…

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