3^(6) - 1^(6) = 12^(3) - 10^(3)
i.e. a^(2n) - b^(2n) = c^(n) - d^(n)
give more examples like this if a & b is not having any common factor between them & n is an odd prime number.
2006-10-16 03:15:19 · 3 answers · asked by rajesh bhowmick 2 in Science & Mathematics ➔ Mathematics
Are you sure there aren't more restrictions on the initial conditions of the problem?
Note trivially that if c = a^2 and d = b^2, the equation is always true:
a^(2n) - b^(2n)
= (a^2)^n - (b^2)^n
For instance, 4^6 - 3^6 = (4^2)^3 - (3^2)^3 = 16^3 - 9^3
and 7^10 - 5^10 = (7^2)^5 - (5^2)^5 = 49^5 - 25^5
Also, your example 3^(6) - 1^(6) = 12^(3) - 10^(3)
also equals (3^2)^3 - (1^2)^3 = 9^3 - 1^3
2006-10-16 03:42:18 · answer #1 · answered by Scott R 6 · 1⤊ 0⤋
The relation is valid for any, c=a^2,d=b^2,
eg:- 10^6-3^6=100^3-9^3
I think You explored the relation & probably haven't got it in any book. Its always easier for us to point out the mistake,but its a lot harder to explore a fact. try on. Who knows if you can reveal some true magic.
2006-10-22 08:34:08 · answer #2 · answered by s0u1 reaver 5 · 0⤊ 0⤋
7^(8)+8^(4)=9^(3)-6^(8)
2006-10-20 23:11:23 · answer #3 · answered by Anonymous · 0⤊ 0⤋