# 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

Posted in Math Beauty, Number Puzzles | Tagged | 10 Comments

## 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 | | 1 Comment

## 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

Posted in Word Puzzle | | 2 Comments

## 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