**new inventions in number theory**.. it proves

**pythagorus-theorem**and

**small-power-Fermat’s-theorems**, finds

**powerfreeness**. Its just like the recently talked about

**ABC conjecture**[my formulation is

**n^{k+1} = 5*m+P where P E {-k .. 0 .. k}**, so you see only 3 integers? ABC {n, k, m}. also extends to nonintegers. 5 is prime. So by formulating higher primes one can prove Fermat’s theorem in few lines not … 500 pages. [

**potentially possible**] If that can be formulated, I haven’t done, but Pythagorus I proved in 1 line. It was proved by some lengthy procedure a page or two. [

**Proof by infinite decent and Fermat’s last proof**]

I invented this new theorem

**couple years ago**, its**basics**, and worked out its detail last year .. it gives**interesting corollaries**:1. a number is not a power of 6 if it’s last two digits are not one of these: 16, 36, 56, 76 or 96, always … OR integer whose 2nd digit to left from right is any odd numbers less than 10 (1,3,5,7..etc)

2. a number is not a power of 5 if it’s last two digits are not 25

3. for powers of 4, always either a 4 or a 6 in the last digit (which adds upto 10)

4. powers of 7: last digit is always an odd number less than 10 but not 5.

5. for powers of 3 is same as that of 7 but their 2nd last digit differ..

There may be some more. I am reading this long article of mine .. [Mohan’s Generalized 50-cent theorem, a new step in number theory]