use division algorithm to show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8?
Added by Alexander H.
Step 1
By the division algorithm, we can write n = 9q + r, where q is an integer and the remainder r satisfies 0 ≤ r < 9. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Nick Johnson and 89 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use Euclid's division lemma to show that the cube of any positive integer is of the form $9 m, 9 m+1$ or $9 m+8$.
Real Numbers
Introduction
Use Euclid's division lemma to show that the square of any positive integer is either of the form $3 m$ or $3 m+1$ for some integer $m$. [Hint : Let $x$ be any positive integer then it is of the form $3 q, 3 q+1$ or $3 q+2$. Now square each of these and show that they can be rewritten in the form $3 m$ or $3 m+1 .]$
If $x^{n}$ is a perfect cube, then $n$ is divisible by what number?
Factoring Polynomials
Factoring Binomials and Perfect Square Trinomials
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD