This is valid till the prime number 5 is sufficient to test the powerfreeness of another integer. {m,n,k} are numbers/integers in the vicinity and for very high powers in Fermat’s theorem one needs higher prime numbers. This theorem has been evidently tested for small powers.

# prime numbers

## new inventions in number theory .. [summary]

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..

## a new step in number theory

“Nature may speak mathematics but it’s often quiet …”

… Or in words: The integer powers of any integer is a multiple of a prime number within a integer scope of the power-integer.

I have explored only the prime number 5 for which I have verified in detail that this is valid. It has many implications including towards Fermat’s theorem and Pythagorean theorem and many more corollaries with great importance towards computational number theory.

I will give a history of how i came to discover this an why I call it by the name of 50cent a celebrated HipHop musician. I am a hiphop musician but nobody knows me. …

## a new step in number theory

“Nature may speak mathematics but it’s often quiet …”

… Or in words: The integer powers of any integer is a multiple of a prime number within a integer scope of the power-integer.

I have explored only the prime number 5 for which I have verified in detail that this is valid. It has many implications including towards Fermat’s theorem and Pythagorean theorem and many more corollaries with great importance towards computational number theory.

I will give a history of how i came to discover this an why I call it by the name of 50cent a celebrated HipHop musician. I am a hiphop musician but nobody knows me. …