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# factorization question

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(2 + 3)(2^2 + 32)(2^4 + 3^4)(2^8 + 3^8)(2^16 + 3^16)(2^32 + 3^32)(2^64 + 3^64) is equivalent to 2^x + 3^y. Compute x and y.

Nov 14, 2021

#1
+13718
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$$(2 + 3)(2^2 + 3^2)(2^4 + 3^4)(2^8 + 3^8)(2^{16} + 3^{16})(2^{32} + 3^{32})(2^{64} + 3^{64})\\ \color{blue}=1.17901845777\cdot 10^{61}=2^x+3^y$$

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Nov 14, 2021
edited by asinus  Nov 14, 2021
#2
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I was looking for x and y, not the actal answer.

Nov 14, 2021
#3
+13718
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I don't know of any solution.

asinus  Nov 14, 2021
#5
+117447
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You can expand it out. Replace the 2 with a and the 3 with b

I suppose you could just expand it out but there is probably a better method

$$(a^{2^0}+b^{2^0})(a^{2^1}+b^{2^1})(a^{2^2}+b^{2^2})(a^{2^3}+b^{2^3})(a^{2^4}+b^{2^4})(a^{2^5}+b^{2^5})\\$$

Nov 14, 2021