SOLUTION: given two odd integers 'a' and 'b'.prove that a^3-b^3 is divisible by 2^n iff a-b is divisible by2

SOLUTION: given two odd integers 'a' and 'b'.prove that a^3-b^3 is divisible by 2^n iff a-b is divisible by2

Algebra.Com

Question 473651: given two odd integers 'a' and 'b'.prove that a^3-b^3 is divisible by 2^n iff a-b is divisible by2
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
given two odd integers 'a' and 'b'.prove that a^3-b^3 is divisible by 2^n iff a-b is divisible by 2
----------------
If a and b are odd, then a-b is always divisible by 2.
------
For what value of n?

RELATED QUESTIONS
Prove that if �a� and �b� are odd positive integers, then a2+b2 is even but not divisible (answered by richard1234)

Let a,b,c be integers such that a^2+b^2 = c^2. For c divisible by 3, prove that a and b... (answered by ikleyn)

I am having a lot of trouble with these proofs; I get so far and alskdjfl.... prove or (answered by khwang)

suppose and b are integers such that 2+a and 35-b are divisible by 11prove that a+b is... (answered by Alan3354)

If a number is divisible by 2 and 3, it must also be divisible by 6. a. True (answered by checkley71)

Classify each of the following as true or false: (a) If a number is divisible by 6, then (answered by richwmiller)

Suppose a positive integer n is divisible by 21 and by 9. What is the smallest possible... (answered by Edwin McCravy)

there are some positive integers n such that n^3 -7 is divisible by n-3 . how many such... (answered by drk)

Let $P(x)$ be a nonconstant polynomial, where all the coefficients are nonnegative... (answered by jim_thompson5910)