Mysterious Primes

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)On analysis of prime numbers I found following few unique relationship which  I couldn’t find anywhere else. Few Unique Relationship between two Prime Numbers: If both P1 & P2 are prime numbers then: (P1^P2+P2^ P1) MOD P1*P2 = P1+ P2 I had posted this as a question on Yahoo Answers  community & following is the proof given by Dannix. Let P1=p and P2=q. Proof: From Fermat’s Little Theorem we have q^p ≡ q (mod p) p^q ≡ p (mod q) Also it is trivial that, q^p ≡ q (mod q) p^q ≡ p (mod p) By the Chinese Remainder Theorem we get q^p ≡ q (mod pq) p^q ≡ p (mod pq) Adding the two congruences yields q^p + p^q ≡ q+p (mod pq) Q.E.D  ...

New way to find Pythagorean Triples...

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)How to find all possible triples from only one side of right angle triangle LOGICAL EXPLANATION My formula is based upon the following equality Hence if D is chosen in such a manner that it is a factor of x2 then we will always have integer values for  Pythagorean Triples since D will get canceled from numerator  &  denominator  Moreover D should be such that X2 / D is ‘Odd’ if D is Odd or it is ‘even’ if D is ‘even’ since even +/- even = even & odd +/- odd =even, denominator’s 2 will also get canceled. We should note that  D can also be greater than X, since we get negative value in such cases we should take absolute figure. Thus if, First side of triple = X then, Second Side = |(X2 – D2)/2D| Hypotenuses =  (X2 + D2)/2D For defining solution set for D, we first have to express X in terms of 2n * y. (where y is an odd number) Let set ‘A’ contain factors of y2 Solution set for D =  {21 * all members of set A U 22 * all member of set A  U … 2n * all member of set A} (Here ‘U’ stands for union)  [Note:- While solving last part (i.e. 2n * all member of set A), one should stop as soon as 2n * any member of A = X and remaining members of A need not be consider since they will give same answer as first half element of that particular subset.] Examples: 1) if X = 35 then it means X = 20 * 35 hence  y = 35. Hence set A will contain factors of 352 i.e. {1,5,7,25,35,49,175,245,1225} However Solution set for D will be {1,5,7,25} [as 20*5th element of set = 35 we need to consider only till 4th element]. Hence there will be 4 triples having 35 as one of the sides. Triples in this case will be (35,612,613),(35,120,125),(35,84,91),(35,12,37) 2) if X = 24 then it means X =  23 * 3 hence y = 3....

Denmark Kangaroo Orange Trick & Mathematical vs Real Life Probability...

VN:F [1.9.22_1171]please wait...Rating: 4.5/5 (2 votes cast)A Brain Teaser which is very popular on net goes as below: 1. pick a number between 2 and 9 2. multiply it by 9 3. add the two digits in the new number not counting their place values 4. minus 5 from that answer  5. every number stands for a letter 1 – A, 2 – B, 3 – C, find your letter 6. think of a country that starts with that letter  7. take the last letter of that country and think of an animal  8. take the last letter of that animal and think of a fruit Now let’s analyze the problem step by step: First part: Guess a number and Multiply it with 9, then add its digits and reduce 5 from it. This part is just a simple distraction to make you feel you are doing something complex. As many of you may know multiplying any number by 9 and adding its digits till you get a single digit will always result in 9. (visit http://mathforum.org/library/drmath/view/67061.html for more information) Now when you remove 5 from 9, you are always left with 4 and Fourth letter of alphabet is “D”, As you may know: (1) You have four countries starting with “D” (a) Denmark (b) Djibouti (c) Dominica (d) Dominican Republic Hence Mathematically you will agree that you have 1/4 chances of selecting Denmark (2) Now If you have selected Denmark then what is the chance that you will select Kangaroo in the next round? Well you have following choices (a) Kangaroo (b) Kaffir cat (c) Kafue flats lechwe (d) Kelp gull (e) Killer whale (f) Kinkajou (g) Kirk’s dik dik (h) Klipspringer (i) Koala (j) Komodo dragon (k) Kongoni (l) Kudu So you have...

Five cool tools that help you untangle World Wide Web Sep15

Five cool tools that help you untangle World Wide Web...

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)Today we live in a world where we crave for more and more refined and intelligent information. Computational Knowledge Engines like Wolframalpha has also changed the way we used to collect information. Although our favorite search engines are becoming increasingly intelligent to do so, we still need to collect, refine, organize and share relevant information. In this post we are going to discover few cool tools that will help you to untangle World Wide Web. (1)   Wepware: A new rising star and surely a game changer, Wepware is a must have tool in your weaponry. Wepware is a chrome based browser extension that comes with loads of cool features. It allows you to capture, organize, share and discover the best parts of the Internet and world around you. It’s our number one choice because unlike other tools which can capture specific content type, Wepware allows you to grab only the relevant part of the website and you can still have full functionality of the website. You can pin your grabs on any webpage and Wepware will reload them when you revisit the page. This opens up endless possibilities. You can capture flash based game or interactive Java Applet. With iGoogle gone, you can use Wepware to create personalized homepages. Grab as you search and browse through the web and let Wepware store content for you. You can access content from anywhere, even from mobile using their Android applcation. You can group related content in a folder or create a personalized “Bind”. Share it with social networking sites or to your private group on Wepware itself. It features Pinterest like familiar and intuitive layout for displaying your grabs. Bloggers can create and share blog post with interactive tools. Wepware...

Art and Science of Walking...

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)Quickbits Section: Read & Learn Walking, the most common activity which we do in our routine life, is so natural that it is more easier than standing. (Here is what Wikipedia has to say about walking).  Following are some of the quick facts which you might not know about walking: Walking is a social phenomenon , you can walk more without tiring if you have got a company. Walking is cyclic activity, we can walk by transferring our body repeatedly from  state of balance to state of imbalance and vise versa. This cycle is known as Gait Cycle. Arm movement plays important role in walking, pendulum like movement of hands eases the effort required for walking. Stride as a verb means to walk with brisk pace with long steps while as noun it just means long steps. When you are walking in crowded areas or places with obstacles, your mind is much more active as it automatically calculates adjustment required to avoid collision. Walking is easier than Standing Still. Why so?  When we walk at a steady pace, we are constantly changing the pressure on each foot. At no point you have both feet flat on the ground.  That alternation of stress and relaxation has two effects. First, it gives your foot a little rest before having to exert a force again, each time you step. Add all those little rests together and you’ll see you spend roughly half your walking time off your feet. The other effect is that walking helps circulate the blood. It’s the increased difficulty in circulation when you are standing still that causes blood to pool a little in your feet. When not enough fresh blood reaches those muscles, they tend to become uncomfortable. This phenomenon is also...