It was a fine day in my college, except for the boring lecture I was attending. I was least bothered about the lecturer's' preaching. I was scribbling some random numbers on my notebook and I observed a peculiar property of divisibility of numbers. It is, if the last n-digits of a number is divisible by 2 power n, then the number will also. I was fascinated by this, and I told this to my friend after the lecture. He told me that he already knew this, he said he read it in his text books during school days, but it was totally new to me. Not disappointed; to me, the real fun is not in finding something new for the world, but in something new to the self! Here are some of my other observations.
* A palindrome integer of even length will always be a multiple of 11.
* if (k, m) are co-primes then, k power n, & m are also co primes
* the difference between a number and its reverse will always be 0 or multiple of 9. This can be generalized to, the difference between a number in base N system and its reverse will be 0 or multiple of N - 1.
* log 1 to base 1 is indeterminate.
All these can be proven by mathematical induction, except for the last (which is intuitive)......
