Category: Mathematics
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Two beautiful theorems
Thm-2; In the above expansion the sum of odd coefficient is same as the sum of even coefficient. put x=-1, then from above; 1+∑even- coefficients = ∑odd-coefficients = 1/2(∑all-coefficients) =
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Proof of Fermat’s theorem in a few lines
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.
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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…
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Does vacuum have time?
Hence Quantum Mechanics allows time to constitute vacuum through a tunnling of the phase-space although the amount of such phase-space is small compared to the amount-of-nothing.
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To Physicists … A question in mind !
To Physicists: do you think “it would be a new invention that uncertainty relations do not (necessarily) follow from non-commutation, the non-commutation leading to uncertainty relations was just one possible way of proving that simple relations between such non-commuting variables [e.g. momentum and position] exist. One of the reasons for this could be; such uncertainty…
M Dash Foundation: C Cube Learning 