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Prove that the cube of any integer can be written as the difference of two squares
Chapter 1, Problem 1.4(choose chapter or problem)
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QUESTION:
Prove that the cube of any integer can be written as the difference of two squares. [Hint:Notice thatn3 = (13 + 23 + + n3) - (13 + 23 + + (n - 1)3). ]
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QUESTION:
Prove that the cube of any integer can be written as the difference of two squares. [Hint:Notice thatn3 = (13 + 23 + + n3) - (13 + 23 + + (n - 1)3). ]
ANSWER:Step 1 of 4
Let us consider a is any integer.
Claim that , where p and q are any integers.
Consider and add, subtract the number
in
we get
As we know that,
By using above formula calculate, we have
Similarly, calculate