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Fifty Lectures for American Mathematics Competitions PDF  Form

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hi everyone in this we're gonna solve 2 to the power of 18 minus 1 equals what so first of all we're going to split this we are going to write it as 2 to the power of 9 times 2 is 18 so we know that 9 times 2 so we can write it like this 2 to the power of 9 times 2 is 18 minus 1 so what I have used here a to the power of n whole to the power of M is equal to a to the power of n times m so here you have the product of the power so you can split it in this way now what does it look like this is in a form of an identity a square point is b square which is equal to a plus b times a minus B now we're going to solve for that so we have 2 to the power of 9 plus 1 times 2 to the power of 9 minus 1. and then as we know 2 to the power of 9 is equal to 512 so we're going to substitute that 512 plus 1 times 512 minus 1. so 512 plus 1 is 513 and 512 minus 1 is 511. so now we are just gonna split this both into 500 plus 13 times 500 plus 11. and now we're gonn

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