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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: June 2013
Patterns  11, 1111, 111111, …
Note the pattern: 11 = (1 * 9) + 2 1111 = (123 * 9) + 4 111111 = (12345 * 9) + 6 11111111 = … Continue reading
A^5 + B^5 + C^5 = X^5 + Y^5 + Z^5 (Part 1)
(1) A^5 + B^5 + C^5 = X^5 + Y^5 + Z^5 A + B = X + Y … Continue reading
Generating Pythagorean triples #1
Pythagorean triple http://en.wikipedia.org/wiki/Pythagorean_triple There are 16 primitive Pythagorean triples with c ≤ 100 : ( 3, 4, 5 ) ( 5, 12, 13) ( 8, … Continue reading
a^k + 2b^k + 2c^k = d^k, where k = 4, 5
(1) a^4 + 2 b^4 + 2 c^4 = d^4 (2) a^5 + 2 b^5 + 2 c^5 = d^5 (1) 2^4 … Continue reading
Posted in Number Puzzles
Tagged 4th Powers, 5th Powers, Sums of 4th Powers, Sums of 5th powers
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Cube of every integer n
3^3 = 27 = 3^3 – 2^3 – (2)^3 4^3 = 64 = 6^3 – 5^3 – 3^3 5^3 = 125 … Continue reading
Num3er 25  a + b = 25
A + B = 25 = 5^2 Let’s find C so that C + A = x^2 and C + B = … Continue reading
Word puzzle Concatenation  Periodic Table of Elements
Rules of the game: Find words (from the dictionary) and sentences that are the concatenation of the elements so that the ratio of letters used to total number of letters in a word is 1. Start with … Continue reading
Prime Numbers Inequality  prime zeta function at 2
Prime Zeta Function http://mathworld.wolfram.com/PrimeZetaFunction.html Prime zeta function at 2 http://oeis.org/A085548 0.4522474200410654985065… = 1/2^2 + 1/3^2 + 1/5^2 + 1/7^2 + 1/11^2 + 1/13^2 + … Can you prove that 1/2^2 + 1/3^2 + 1/5^2 … Continue reading
Sum of four consecutive cubes  “Near” squares
The cubes : a(n) = n^3 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, … Continue reading
Product  Use the digits 1 to 9 exactly once
Goal: To use all digits from 1 to 9 de a b c fg hi where each of 9 the letters (a, b, c, d, e, f, g, h, i) represents … Continue reading