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Sum of consecutive numbers - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/number-prompts/sum-of-consecutive-numbers
It follows that the number of ways of expressing a number as the sum of consecutive positive integers is (q + 1)(r + 1) - 1. Examples. 45 as the product of ...

Difference of two cubes - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/algebra-prompts/difference-of-two-cubes
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Explore the cubes of non-consecutive numbers;. Make and prove generalisations ...

Vandita Patel - Publications

https://sites.google.com/view/vanditapatel/publications
On perfect powers that are sums of two Fibonacci numbers, with F. Luca ... Perfect powers that are sums of consecutive cubes, with M. A. Bennett and S ...

Cube numbers - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/algebra-prompts/cube-numbers
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers inquiry. The prompt. Mathematical inquiry processes: Verify ...

Squares and cubes - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/number-prompts/squares-and-cubes-inquiry
The prompt invites students to identify and extend a pattern using the sum of consecutive cubes. Students can follow different lines of inquiry.

‪Vandita Patel‬ - ‪Google Scholar‬

https://scholar.google.com/citations?user=cJRFyLYAAAAJ&hl=en
Journal of Number Theory 189, 90-96, 2018. 42, 2018. Perfect powers that are sums of consecutive cubes. MA Bennett, V Patel, S Siksek. Mathematika 63 (1), 230 ...

‪Vandita Patel‬ - ‪Google Scholar‬

https://scholar.google.com/citations?user=cJRFyLYAAAAJ&hl=tr
On perfect powers that are sums of two Fibonacci numbers‏. F Luca, V Patel ... Perfect powers that are sums of consecutive cubes‏. MA Bennett, V Patel, S ...

Proof Without Words: Perfect Numbers and Sums of Odd Cubes

https://sites.google.com/a/lclark.edu/nelsen/oddcubes.pdf?attredirects=2
We show wordlessly that every even perfect number greater than six is a sum of consecutive odd cubes. ROGER NELSEN (MR Author ID: 237909) is professor emeritus ...

Vandita Patel - Talks/Conferences

https://sites.google.com/view/vanditapatel/talksconferences
Descent of a Sum of Consecutive Cubes ... Twice!!, Junior Number Theory Seminar - University of Oxford, 09/05/2016. Graphing Congruences of Newforms (Poster) ...

Pranabesh Das - Research Articles

https://sites.google.com/site/pranabeshdas2124161605/research-articles-1
Rout, Perfect powers in Alternating sums of consecutive cubes, Glasnik ... Das and JC Saunders, Products of Tribonacci Numbers that are the Products of Factorials ...

Difference of two squares - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/algebra-prompts/difference-of-two-squares-inquiry
They did achieve this by the end of the lesson and were working on proving the difference of consecutive cube numbers. I introduced a related prompt (below) to ...

A reply to Mr Barton - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/blog-posts/a-reply-to-mr-barton
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers · Difference of two cubes · Difference of two squares.

Inquiry and online learning - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/blog-posts/inquiryandonlinelearning
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers · Difference of two cubes · Difference of two squares.

Proof - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/algebra-prompts/proof
Cube numbers · Difference of two cubes · Difference of two squares ... The sum of the first three consecutive even integers (two, four, and six) is ...

Sum of unit fractions - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/number-prompts/unit-fractions
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers · Difference of two cubes · Difference of two squares.

Triangular numbers - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/algebra-prompts/triangular-numbers
Cube numbers · Difference of two ... A further step would be to prove algebraically that the sum of two consecutive triangular numbers is a square number.

How to get started with Inquiry Maths - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/blog-posts/how-to-get-started-with-inquiry-maths
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers · Difference of two cubes · Difference of two squares.

Indices - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/number-prompts/indices-inquiry
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... What happens if we cube the counting numbers? Use the same base and change ...

Graphs of functions - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/algebra-prompts/graphs-of-functions
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers · Difference of two cubes · Difference of two squares.

The differences between investigations and inquiries - Inquiry Maths

https://sites.google.com/site/inquirymaths/home/blog-posts/thedifferencesbetweeninvestigationsandinquiries
Sum of consecutive numbers · Sum of unit fractions · Surds · Algebra prompts ... Cube numbers · Difference of two cubes · Difference of two squares.