Mathematics

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Wednesday, September 14, 2011

Adding to prime number

What elementary principle of algebra allows us to know almost instantly that the following calculated integers are prime? Note; 2^2 = 2*2 = 4; 2^3 = 2 * 2 * 2 = 8; etc. 2+3, 2^2 + 3 2^3 + 3 2^4 + 3 2 + 3^2 2^2 + 3^2 2^3 + 3^2 2*3 + 5 2*5 + 3 3*5 + 2 2^2 * 3 + 5 2^3 * 3 + 5 2 * 3^2 + 5 2^2 * 3^2 + 5 Sign in to see full entry.

Friday, September 9, 2011

Thinking algebraically

One time I listened to a student explain why he had difficulty with algebra. "I can work fine with numbers. It makes sense to me to add two numbers to me. It does not make sense to add two letters. It confuses me." So I said, When we write "A + B", we are not merely adding the letter A to the letter... Sign in to see full entry.

Tuesday, September 6, 2011

What's special about integers 11 through 20?

What's special about integers 11 through 20? http://www.daviddarling.info/encyclopedia/N/numbers_types.html 11 is the smallest repunit prime. http://en.wikipedia.org/wiki/Repunit_prime#Repunit_primes 12 is the smallest abundant number. http://www.daviddarling.info/encyclopedia/A/abundant_number.html... Sign in to see full entry.

What's special about each of the integers 1,2,3,4,5,6,7,8,9,10?

http://www2.stetson.edu/~efriedma/numbers.html http://www.goiit.com/posts/list/0/community-shelf-every- number-is-special-78754.htm http://www.numbergossip.com ---------------------- 0 is the additive identity. http://en.wikipedia.org/wiki/Additive_identity 1 is the multiplicative identity.... Sign in to see full entry.

Monday, September 5, 2011

The impossible puzzle

http://en.wikipedia.org/wiki/Impossible_Puzzle The Impossible Puzzle, also named Sum and Product Puzzle is a puzzle called "impossible" because it seems to lack sufficient information for a solution. It was first published in 1969,[1] and the name Impossible Puzzle was coined by Martin Gardner.[2]... Sign in to see full entry.

Sunday, September 4, 2011

Mathematical Jokes

Mathematical Jokes Selected from: http://www.math.utah.edu/~cherk/mathjokes.html ---------------------------------- A mathematician, a physicist, an engineer went again to the races and laid their money down. Commiserating in the bar after the race, the engineer says, "I don't understand why I lost... Sign in to see full entry.

Saturday, September 3, 2011

Sum of same power of consecutive integers

Sum of same power of consecutive integers. How would we find the formula for the sum 1 + 2 + 3 +... + n, where the value of n is not yet specified? One approach is to examine the first few sums and look for a pattern. 1 = 1 = 1 * 1 1 + 2 = 3 = 1 * 3 3 + 3 = 6 = 2 * 3 4 + 6 = 10 = 2 * 5 5 + 10 = 15 =... Sign in to see full entry.

Friday, September 2, 2011

Applying Algebraic identities to simplify arithmetic

Consider the algebraic multiplication of (A-B) and (A+B). (A-B)*(A+B) = A*(A+B) - B*(A+B) = A*A + A*B - B*A - B*B = A*A -B*B In words, the product of the difference and sum of two numbers is the difference of their squares. Quick, what is 29*31? 29 is the difference of 30 and 1. 31 is the sum of 30... Sign in to see full entry.

Thursday, September 1, 2011

Math puzzle 001

What number, between 1 and 100, has remainder 1 when divided by 2, has remainder 2 when divided by 3, has remainder 3 when divided by 4 or 7 or 8, has remainder 4 when divided by 5, has remainder 5 when divided by 6 or 9? Sign in to see full entry.

Wednesday, August 31, 2011

Logic puzzle 001

You see that some one has broken the lamp in the living room. You've just completed the course led by the main character in the "lie to me" show, and now have confidence that you can tell which of your children are lying when they answer your questions. The four children give the following answers,... Sign in to see full entry.

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