# Mathematics

### Monday, August 25, 2014

#### Magic Squares 5 by 5

Hello This is my most recent work. Example of the 5 by 5 magic square is 573 486 518 556 257 570 576 545 273 426 245 213 478 590 864 498 878 564 185 265 504 237 285 786 578 The 5 rows add to the magic number. 573+486+518+556+257=2390 570+576+545+273+426=2390 245+213+478+590+864=2390... Sign in to see full entry.

### Wednesday, May 7, 2014

#### Easy arithmetic puzzle

Name the smallest 3 digit positive integer such that the sum of its digits = 4. Sign in to see full entry.

### Thursday, May 1, 2014

#### What is mathematics

Here is a good explanation of mathematics. http://www.maa.org/external_archive/devlin/devlin_06_10.html In Math You Have to Remember, In Other Subjects You Can Think About It The title is ironic because the point of the article that math is a way of thinking. Sign in to see full entry.

### Saturday, April 26, 2014

#### Determined by remainders

A positive integer between 1 and 50 has remainder 1 when divided by 3, remainder 2 when divided by 5,and remainder 4 when divided by 11. What is that integer? Sign in to see full entry.

### Wednesday, April 23, 2014

#### Average velocity

Adrian must get to his destination, sixty miles away, in exactly one hour. His average speed for the first half of his journey is 30 miles per hour. How fast must he go to make it on time? Bill averaged the first half of his journey at 40 miles per hour. He averaged the second half of his journey at... Sign in to see full entry.

### Saturday, April 12, 2014

#### Simple Arithmetic puzzle

The product of two positive integers is 187. What is their sum? There are two possible answers to the puzzle. Sign in to see full entry.

### Thursday, April 10, 2014

#### A novel way to derive the factoring of 63 = 7 * 9

Algebraic parity analysis of factoring of 63. Solve x0 * y0 = 63. The factoring of 63 = 3 * 3 * 7 is trivial, but here I am illustrating a novel way to derive the factoring. 63 is odd. Both x0 and y0 are odd. Set x0 = (2 x1 + 1) y0 = (2 y1 + 1) (2 x1 + 1) (2 y1 + 1) = 63 4 x1 y1 + 2 x1 + 2 y1 + 1 =... Sign in to see full entry.

### Sunday, April 6, 2014

#### Fermat Factoring by difference of squares

A classical algorithm for factoring a positive integer z is to find two squares, t^2 and s^2, such that t^2 - s^2 = z. 65 = 5 * 13 65 = ((13+5)/2)^2 -((13-5)/2)^2 65 = 9^2 - 4^2 65 = 81 - 16 If z = x y if and only if z = ((y+x)/2) )^2 - ((y-x)/2)^2 z = t^2 - s^2 if and only if z = (t-s)(t+s). To... Sign in to see full entry.

### Friday, April 4, 2014

#### Divisibility tests

A positive integer, written in base 10, is divisible by 2 if and only if its rightmost digit is divisible by 2. A positive integer, written in base 10, is divisible by 3 if and only if the sum of its digits is divisible by 3. A positive integer, written in base 10, is divisible by 4 if and only if... Sign in to see full entry.

### Wednesday, April 2, 2014

#### Spliting the pie

Dan, Mary, and Paula were given choices of how much of each small pie they wanted. Dan: I want half of a pie. Mary: I want a third of a pie. Paula: I want a fourth of a pie. How many pies were needed to give Dan, Mary, and Paula, exactly what they wanted? Sign in to see full entry.