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Is the positive integer n divisible by 6?
n is a positive integer that is divisible by 6. A)The quantity in Column A is greater. B)The quantity in Column B is greater….Show timer Statistics.
Quantity A | Quantity B |
---|---|
The remainder when n is divided by 12 | The remainder when n is divided by 18 |
How do you prove a number is divisible by 3?
Divisibility by 3 or 9 First, take any number (for this example it will be 492) and add together each digit in the number (4 + 9 + 2 = 15). Then take that sum (15) and determine if it is divisible by 3. The original number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).
What is the form of any positive integer?
Hence, Any positive integer is of the form 3q or 3q + 1 or 3q + 2, where q is some non-negative integer.
Where m is some integer 8 for any positive integer n prove that N 3 N is divisible by 6?
Out of three (n – 1), n, (n + 1) one must be even, so a is divisible by 2. 2. (n – 1) , n, (n + 1) are consecutive integers thus as proved a must be divisible by 3. Thus, n³ – n is divisible by 6 for any positive integer n.
How to prove n^3 – n is divisible by 6?
Prove that for any positive interger n, n^3 – n is divisible by 6. there are two methods to solve the problem which are discussed below. 1. Out of three (n – 1), n, (n + 1) one must be even, so a is divisible by 2. 2. (n – 1) , n, (n + 1) are consecutive integers thus as proved a must be divisible by 3.
How do you know if a number is divisible by 2?
∴ n = 2q or 2q + 1, where q is some integer. Then n is divisible by 2. n+1= 2 (q + 1) is divisible by 2. So, we can say that one of the numbers among n, n – 1 and n + 1 is always divisible by 2. ∴ n (n – 1) (n + 1) is divisible by 2.
What is the divisibility rule of 6?
Since, n (n – 1) (n + 1) is divisible by 2 and 3. Therefore, as per the divisibility rule of 6, the given number is divisible by six. n 3 – n = n (n – 1) (n + 1) is divisible by 6. Was this answer helpful?
What is the inductive step of the divisibility test?
Inductive Step:Assume that P ( k) is true; i.e. k 3 − k is divisible by 3. To complete the inductive step, we must show that when we assume the inductive hypothesis, it follows that P ( k + 1), the statement that ( k + 1) 3 − ( k + 1) is divisible by 3, is also true.