n(n^2-1) is always divisible by?
531909
Thank you. n(n^2-1 ) is always divisible by 24 for all odd numbers..
645257
The numbers that 22 is divisible by are 1, 2, 11, and 22. You may also be interested to know that all the numbers that 22 is divisible by are also known as the factors of 22. Not only that, but all the numbers that are divisible by 22 are the divisors of 22.
672799
(10 points) Prove that 10n+1 + 10n + 1 is divisible by 3 for n ∈ N. Solution: If n = 1, then 10n+1 + 10n + 1 = 111 is divisible by 3. ... Therefore, the statement is true for all natural numbers by the Principle of Mathematical Induction.
1415904
We have calculated all the numbers that 29 is evenly divisible by. The numbers that 29 is divisible by are 1 and 29 and 29.
1122044
You can make every odd number by taking consecutive squares. (n+1)^2 - n^2 = 2n+1, every odd number can be written in the form 2n+1. ... Thus, a number n can only be a difference of two squares if it has two factors of the form (a + b) and (a - b), where a + b \geq \sqrt{n} and a - b \leq \sqrt{n}.
634135
All numbers divisible by 4 are divisible by 2 . But all numbers divisible by 2 are not divisible by 4.
1030538
Any n can be written as n = 10k + u where u is the units digit of n. ... Prove that n6 – 1 is divisible by 7 if (n,7) = 1. Proof: By Fermat's Theorem if (n,7) = 1 then since 7 is prime.
63304
Divisibility by 2, 4, and 8 All even numbers are divisible by 2. Therefore, a number is divisible by 2 if it has a 0, 2, 4, 6, or 8 in the ones place. For example, 54 and 2,870 are divisible by 2, but 2,221 is not divisible by 2. A number is divisible by 4 if its last two digits are divisible by 4.
1294703
Is 4 -1 divisible by 3? Yes 3 is divisible by 3. If 4^n-1 is divisible by 3, it can be written as 4^n -1 = 3*k, where k is an integer.
640342
It is quite easy to prove that squares are either 0 or 1mod4, so n2−2 is either −2 or −1mod4, and thus, n2−2 cannot be divisible by 4.
462052
A number is divisible by 7 if it has a remainder of zero when divided by 7. Examples of numbers which are divisible by 7 are 28, 42, 56, 63, and 98.
1313017
This means that 5n – 1 = 4a for an integer a. Then Prove: 5n+1 – 1 is divisible by 4. This means to prove that 5n+1 – 1 = 4b, for some integer b.
1276065
If 4^n-1 is divisible by 3, it can be written as 4^n -1 = 3*k, where k is an integer. 4^(n+1) -1 = 4 * 4^n -1 = 4 * (4^n -1 + 1) -1.
728021
Divisible means exactly divisible and the quotient of the division has to be an integer with no remainder. Since 1 is not divisible by 2 , it is an odd number. You can also say that a number which can not be divided evenly by 2 is an odd number. ... Hence, 1 is an odd number.
308391
A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156. [We know the rules of divisibility by 2, if the unit's place of the number is either 0 or multiple of 2]. 42 is divisible by 2.
800624
Simply: If n is odd, n^2 is odd so n^2 + 2 must be odd. If n is even, n^2 is a multiple of 4 so n^2 + 2 cannot be a multiple of 4 (will have remainder 2). If n is pair ( = 2m ) then n^2+2 = 4m^2 + 2; thus not divisible by 4.
1233425
The degree of the remainder is always less than the degree of the divisor in case of polynomial division. ... But degree of (y+5) is 1. So it can't be the remainder.