is it true i think it is what do u think?

Question

a^(n)-b^(n)
=(a-b)^(n)+nk(a-b)
here when "a" is an odd natural number,"b" is any natural number other then "a" and "n" is any prime or its factors are the same prime then "k" will always be a natural number.

Answer 1

no not true.. a counterexample is a=1,b=1,n=2, then K can be any number including PI wich is not natural.

if you dont want a and b equal then it is true :

a^(n)-b^(n) -(a-b)^(n) = nk(a-b)

a,b,n are natural numbers, the left side is a natural number thus K must be a natural number for equality.

Any expression in natural numbers where the expression only has the operator +, - * and ^ , is when evaluated a natural number,

Answer 2

no 2 people on this earth can think a like, we say sometimes i just thought to say the same thing, but it might not be in the same words. it is not proven scientifically that 2 people think alike.
The view of humans as both immanent in, and transcendent to, nature is ‘slightly odd’ because it seems to suggest that ‘things like consciousness, agency and free will are real’ but ‘beyond scientific… explanation’. if consciousness, agency and free will can be explained mechanistically they will be exposed as illusions: in other words, that the belief in the reality of consciousness and agency and in a mechanistic science are mutually exclusive. My own view is neither that consciousness, agency and free will are illusions, nor that they are beyond scientific explanation, but rather that they cannot be fully explained by the precepts of natural science. This is the key point of difference.

Answer 3

Yes. It is true. Can be proved using bionomial expansion

Answer 4

Not true

Answer 5

Not true.

Answer 6

it is true provided a>b.

Answer 7

it is not true