Can't quite tell what you mean by n3.
1) If that's n3, then:
If n3 is even, it can be expressed as n * n * n = 2 * t (t is a natural number).
You can see that two is a factor of n3, and so it has to be a factor of n, because there is no ther number that could contribute to it. So n is even too.
2) If you mean 3 * n, then:
3 * n = 2 * t, where t is a natural number.
Again, the only number to contribute factor 2 for the right side of equation is n.
So n has to be even too.
The statement n3 is ambiguous. I presume you mean n3, which means n cubed or n to the power of 3 (n*n*n). However, n3 (which should really be written as 3n) means n times 3 (n*3).
Here is a method: cube root of 400g = n, where n is an integer cube both sides: 400g = n3 then: g = n3/400 therefore: n3/400 must be an integer if this is so, then n3 must be divisible by 400 with no remainder, and n must be => cube root of 400 which is 7.368 bracket the answer by substitution: let n=8, n cubed = 512 no good let n=12, n cubed = 1728 no good let n=20, n cubed = 8000, 8000/400=20 OK No smaller value of n will be divisible by 400 without a remainder, so g=20 is the smallest positive integer that meets the requirement.
Un = n3 + n2 - 3n - 2 for n = 1, 2, 3, ...
If m * n is even, it can be expressed as m * n = 2 * t, where t is natural number. Either m or n has to provide factor of 2 for the right side of equation, so it basically means at least one of them has to be even.
Call the lowest of the even integers n. Then from the problem statement, n + n + 2 + n + 4 = n + 6 =244. Collecting like terms results in 4n + 12 = 244, or 4n = 244 - 12 = 232, or n = 232/4 or 58. The consecutive even integers are therefore, 58, 60, 62, and 64.
Let any number be n:- n3/n3 = n*n*n/n*n*n = 1 And in index form: n3/n3 = n3-3 = n0 = 1
n3 + 1 = n3 + 13 = (n + 1)(n2 - n + 12) = (n + 1)(n2 - n + 1)
If: n3 = 8 Then: n = 2
N cubed
The formula for the nitride ion is N3-.
n x n2 = n3
6+N3 is the sum of N*3 then you add six. 6*N3 is you multiply 6 times three times N times three.
No even values of n will give give an odd value of n3, so n must be odd.When n is odd, n2 is also odd, so n2+1 must be even. ■
The statement n3 is ambiguous. I presume you mean n3, which means n cubed or n to the power of 3 (n*n*n). However, n3 (which should really be written as 3n) means n times 3 (n*3).
N3-13
n3 + 3n2 + 4n + 12 = (n3 + 3n2) + (4n + 12) = n2(n + 3) + 4(n + 3) = (n2 + 4)(n + 3).
Let the number be n.Then (n3)3 = n3 x 3 = n9.........or n to the power nine.However, if the question is what the the one-third power of a number cubed, then:(n3)1/3 = n3 x 1/3 = n1 = n