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]

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