(3) Prove that if a cube of a number is divisible by 17, then the number is divisible by 17.

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: To show the representation of an even integers is 2k and that for odd integer is 2k+1 or 2k-1 by…

Q: Prove that every natural number can be expressed as a product of an odd integer and a nonnegative…

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Q: Prove that N × N × N is countable. Does your argument generalize to the Cartesian product of k…

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Q: Prove that the cube of any integer has to be exactly one of these forms: 9k, 9k + 1, or 9k + 8 for…

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Q: Show that a positive integer N is divisible by 7 if and only if the difference between twice the…

A: We have to show that a positive integer N is divisible by 7 if and only if the difference between…

Q: Given positive odd integer (a), find all possible divisors, which are always divided a + (a + 1)° +…

A: Odd numbers are those numbers which are not divisible by 2. For example: 3, 5, 7,.... Those numbers…

Q: Fermat's theorem is not true for composite number. Select one: O True O False

A: Ans :  true

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.

A: integer  which have 2 as one of their factors are called even numbers. The integer  which do not…

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: Even number: we say a number 'n' is even if it is divisible by 2. if  'n' is even then it is…

Q: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

Q: Use Wilson's Theorem to verify that 4(29!) + 5! is divisible by 31.

A: The given number is 4 (29)! + 5! . Our aim is to verify that the given number is divisible by 31…

Q: A) Let m=7. How do you find the inverse of all integers from 1 through 6 using the multiplication…

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Q: Are all perfect squares divisible by 2

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Q: Prove that 5n-1 is divisible by 4 to any positive integer n

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Q: Which of the following is a binary operation on the set of positive real numbers? a. a*b = √a + √a+…

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Q: h(x)=2x^4+5x^3+29x^2+80x-48  Zero:-4i The remaining zeros of h are

A: h(x) = 2x4 + 5x3 + 29x2 + 80x - 48 We know, if a complex number is a zero of a polynomial, then its…

Q: Show that every positive integer can be written as the product of a square (possibly 1) and a…

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Q: Prove that for any integer n, we have n - 2 is not divisible by 4.

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Q: Show that for any integer n , n2 – 2 is not divisible by 3.

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Q: If x is divisible by 5 or y is divisible by 5, then xy is divisible by 5.

A: Let x is divisible by 5. Then x=5u for some natural number u.

Q: Prove: If the sum of the digits of a number in base bis divisible by b 1, so is the number.

A: Given statement: Sum of digits of any number (x) in any base b is divisible by b-1. To prove: The…

Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: if a is a positive integer less than 10, then 7a7,7a7,7a7 is divisible by 3 Select one: O True O…

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Q: B. Show that 4n+ 4n+1 + 4n+2 + 4n+3 + 4n+4 is divisible by 11 for any positive integer n. C. Find…

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Q: 2. Prove that the difference of an odd integer and an even integer is odd.

A: Prove that the difference of an odd integer and an even integer is odd