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Competition Entries

# The Next Einstein COMPETITION ENTRY

ENTRY TITLE

##### I have made an algebraic identity
 IDEA BY: Aditya Anand LOCATION: Other CATEGORY: Education

ENTRY TITLE

##### I have made an algebraic identity
 IDEA BY: Aditya Anand LOCATION: Other CATEGORY: Education

ENTRY DESCRIPTION

## The difference between same number with different real number as powers is equal to the product of the sum of the numbers with the powers between them including the lowest number and one subtracted from the number.

For a number A, with powers M and Z, such that, M>Z A^M - A^Z = (A-1) * [(A^N) + ( A^O) ............(A^Y) + (A^Z)] For example, 7^3 - 7^1 = (7-1) * [(7^2) + (7^1)] L.H.S. = 7^3 - 7^1 = 343 - 7 = 336 R.H.S. = (7-1) * [(7^2) + (7^1)] =6 * [49+7] = 6*56 = 336 If we consider one more example, 7^7 -(7^-2) = (7-1) * [(7^6) + (7^5) +(7^4)+(7^3)+(7^2)+(7^1)+(7^0)+(7^-1)+(7^-2)] L.H.S. = 823543 - 0.0204 (approx) = 823542.9796 R.H.S. = (7-1) * [(7^6) + (7^5) +(7^4)+(7^3)+(7^2)+(7^1)+(7^0)+(7^-1)+(7^-2)] = 6 * 137257.1632 (approx) = 823542.9796  