# Highest power of 2

Highest power of two that divided $3^{1024}-1$

I did from binomial and expansion but is there a smarter way ?

My approach : $3^{1024}-1$ can be $(3^{512} + 1)$ and $(3^{512} – 1)$

Again$( 3^{512} – 1 )$ is written as $( 3^{256} + 1 )$ and $( 3^{256} – 1)$ Again $( 3^{256} – 1 )$is written as $( 3^{128} + 1 )$ and $( 3^{128} – 1)$ Again $( 3 ^{128} – 1 )$ is written as $( 3^{64} + 1 )$ and $( 3^{64} – 1)$ Again $( 3^{64} – 1 )$ is written as $( 3^{32} + 1 )$ and $( 3^{32} – 1)$ Again $( 3^{32} – 1 )$ is written as $( 3^{16}+ 1 )$ and $( 3^{16} – 1)$ Again $( 3^{16}– 1 )$ is written as $( 3^{8}+ 1 )$ and $( 3^{8} – 1)$ Again $( 3^(8) – 1 )$ is written as $( 3^{4} + 1 )$ and $( 3^{4}– 1)$ Again $( 3^{4}– 1)$ is written as $(3^{2} + 1)$ and $( 3^{2} – 1)$ Again $( 3^{2} – 1)$ is written as $( 3^{1} + 1 )$ and $( 3^{1} – 1)$ or$2^(2)$and$2^(1)$

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