:: This is not a review about his music and stuff. It is just a blog admiring a particular song for which he had composed the music. The effect of the song might last on me for a day. Thought, will roll out my current state of mind as a post before the euphoria subsides. ::
I had been playing the "Iktara" song (one can even go to the extent of saying that i just listened to this song alone) from "Wake up Sid" for several days (right from the time i had watched the movie). And today my roomie asked me to listen to a song called "Thee Kuruvi" from Kangalal Kaidu Sei (Tamil movie). I had listened to this particular song before this day. But, i never gave much attention to the lyrics nor to the small interludes of different musical instruments which ARR had used while composing the song.
I found the lyrics of this particular song amazing. The music is top class, amazing and awesome. Particularly, the small interludes in between the singing(although it is a trademark of ARR's compositions, this one looks special) make it even more beautiful. And the relative ease with which Harini sings(/zaps through) the "theekuruviyaay theenkaniyinai" couplet adds "the extraordinary tag" to the song. That particular couplet was an absolute tongue twister and she had sung it magnificently. Right now, as you can guess, this particular song has become the next Iktara of my list.
Saturday, December 5, 2009
Wednesday, December 2, 2009
Some prime number puzzle
One of my friends asked me to solve a basic puzzle. The results I found after solving the same made me to write a blog. Yeah, first the puzzle.
The solution is fairly simple. The factors of LHS is p-1, p+1. One of them is divisible by 2 and the other by 4 (Since, p is odd and out of two consecutive even primes one of them will be divisible by 4). Out of every three consecutive natural numbers, one of them should be divisible by 3. Since p is prime, either of the factors is divisible by 3. And hence the proposition is true.
After this, another colleague told me that prime numbers, greater than 3, can be expressed as 6K+1 or 6k-1. (It is not a sufficient condition, in the sense, all numbers of the given forms needs to be prime). After spending some time, i found out that all the numbers modulo 6 can be expressed as 6q+r and r can range from 0 to 5. Given this, one can arrive at the conclusion that two sets of natural number forms 6q+1, 6q-1 (same as 6q +5) cannot be directly expressed as product of two direct factors. And hence, the prime numbers can fall into the class either of the number forms. So, the hypothesis is valid. I was just hunting for other numbers which will be forming such number forms (classes) that can be used for primality testing. I have to devise some sort of strategy to find some other number, which will generate two classes. (Quiet obviously, 2 3 and 4 are already considered). If someone can point me to a good read on the same, it will be awesome.
Later, i moved on to read about Sexy Primes and Twin primes in wiki. The articles were awesome and i loved it :). Also, if possible try reading about Surreal Numbers (just google for it and download a nicely written pdf on the same. this is purely for pleasure reading).
Prove that p^2 - 1 is always divisible by 24 for p being prime and p>=5
The solution is fairly simple. The factors of LHS is p-1, p+1. One of them is divisible by 2 and the other by 4 (Since, p is odd and out of two consecutive even primes one of them will be divisible by 4). Out of every three consecutive natural numbers, one of them should be divisible by 3. Since p is prime, either of the factors is divisible by 3. And hence the proposition is true.
After this, another colleague told me that prime numbers, greater than 3, can be expressed as 6K+1 or 6k-1. (It is not a sufficient condition, in the sense, all numbers of the given forms needs to be prime). After spending some time, i found out that all the numbers modulo 6 can be expressed as 6q+r and r can range from 0 to 5. Given this, one can arrive at the conclusion that two sets of natural number forms 6q+1, 6q-1 (same as 6q +5) cannot be directly expressed as product of two direct factors. And hence, the prime numbers can fall into the class either of the number forms. So, the hypothesis is valid. I was just hunting for other numbers which will be forming such number forms (classes) that can be used for primality testing. I have to devise some sort of strategy to find some other number, which will generate two classes. (Quiet obviously, 2 3 and 4 are already considered). If someone can point me to a good read on the same, it will be awesome.
Later, i moved on to read about Sexy Primes and Twin primes in wiki. The articles were awesome and i loved it :). Also, if possible try reading about Surreal Numbers (just google for it and download a nicely written pdf on the same. this is purely for pleasure reading).
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