# Monthly Archives: December 2012

## Num3ers on Pascal’s triangle

Let   a, b, c, d   be 4 consecutive elements in a row of Pascal’s triangle. Say, for example,   8,   28,   56,   70    (Row 8) Consider the following: a/(a+b)   =   8/(8+28)   … Continue reading

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## Sum of cubes of 3 consecutive integers expressed as sum of consecutive integers

(1) Expressible as a sum of 2 consecutive integers (x – 1)^3   +   x^3   +   (x + 1)^3   =   a   +   (a + 1) 3*x(x^2 + 2)   =   2*a   … Continue reading

## Sum of cubes of consecutive integers expressed as sum of consecutive integers

(1)   Sum of cubes of 2 consecutive integers expressed as sum of 2 consecutive integers x^3 + (x + 1)^3 = a + (a + 1) 2*x^3 + 3*x^2 + 3*x + 1 = 2*a + 1 -2*a + … Continue reading

## Sum of squares of 4 consecutive integers

Sum of squares of 4 consecutive integers expressed as the sum of 5 consecutive integers: (x – 1)^2 + x^2 + (x + 1)^2 + (x + 2)^2   =   (a – 2) + (a – 1) + a … Continue reading

## Sum of squares of consecutive integers expressed as the sum of 2 and 5 consecutive integers

(1)   Sum of squares of 2 consecutive integers expressed as the sum of 2 consecutive integers x^2 +   (x + 1)^2   =   a   +   (a + 1) Solutions: a = n^2 – n,        … Continue reading

## Integer between two consecutive squares

x^2   and   (x + 1)^2   are two consecutive squares. Difference:     (x + 1)^2   –   x^2   =   2*x   +   1 An integer of the form   2*x   +   1 … Continue reading

## On Consecutive Num3ers expressible as sum of 2 squares

Here are the first few numbers from   1   to   50   that are expressible as sum of two squares: 1 = 0^2 + 1                              10 = 1^2 + 3^2 2 = 1^2 + 1^2                         13 … Continue reading

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## Math Art

Tom Wilkinson http://www.tomwilkinson.com/ Green Ray     Wilkinson’s work examines the patterns created by particles in motion. “Green Ray” is an experiment in which spinning lights are used to create the illusion of a solid form, in this case a … Continue reading

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## Prime num3er p = x^n – y^m, n ≠ m

Find prime numbers     p   =   x^n – y^m,    n ≠ m   For example, 776887   is a prime number.     And,    7^7   –   6^6 =   776887 more examples, 15511   is … Continue reading

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## 3-digit num3ers : prime factors

Older post:   2-digit num3ers – prime factors   3-digit prime numbers:   101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, … Continue reading