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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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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
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
Posted in Math Beauty, Number Puzzles
Tagged consecutive num3ers, Sum of two squares
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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
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
3digit num3ers : prime factors
Older post: 2digit num3ers – prime factors 3digit 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
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