what is 3 ^ (17)?

Question

if 3 ^ (9) = 3282 ^ (2) - 3279 ^ (2) express in a similar way 3 ^ (17) in terms of difference of at least one set of two perfect squares.

Answer 1

3 ^ 9 = 3282²-3279²
Let 3 ^ 17 = 3 ^ 9 * 3 ^ 8
=>
3 ^ 17
= (3282²-3279²)*3 ^ 8
={(3^4)*3282²-(3^4)*3279²)}
={9²*3282²-9²*3279²)}
={(9*3282)²-(9*3279)²)}
=(29538²-29511²)

3^17=(29538²-29511²)

Answer 2

Rajesh, what's your problem? u have been asking similar questions over and over again. a number X^n can be expressed as X^n=Y^2-Z^2. So? It's a very obvious thing. What do u want us to do? Recognise your "achievement"?? Declare it a major discovery?? You did not prove FLT. I repeat, u did not. So many people had tried explaining to you where the mistakes in your proof are, why can't you just accept it?? No, it's not we who cannot understand your proof, we do. It's just that, it's wrong!

You want 3^7 in that form?? There a so many possibilities. You can have 3(3^16), u can have 3^2 (3^15), 3^3 (3^14), 3^4 (3^13)....... since 3^n is odd for whatever interger n, (3^n)(3^m) is always expressable in X^2-Y^2 with integer X and Y and u can find X and Y by rewriting thing as (X+Y(X-Y)!!

How r u gonna tackle FLT if u can't even get the basic concepts straight??

Answer 3

Note that a^2 - b^2 = (a+b) (a-b). Like in the 3^9 case we can write 3^17 in the form 3^16 x 3. Therefore a+b = 3^16 and a-b = 3.
Solving for a and b leads to a=21523362 and b=21523359

Answer 4

3^17=129140163

Answer 5

wow its too early in the morning to figure that one out! LOL :)

Answer 6

try doing that manually, it will take time but will perhaps improve ur calculations

Answer 7

use windows calculator in its scientific view then=129140163