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Is it possible to write 3^2016 + 4^2017 as the product of two numbers, both of which are over 2018^183?

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Is it possible to write 3^2016 + 4^2017 as the product of two numbers, both of which are over 2018^183?
posted Feb 20, 2018 by anonymous

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1 Answer

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Essentially it is to be proven that
3^2016 + 4^2017 > (2018^183)^2
3^2016 + 4^2017 > 2018^366
4^2017 = 2^4034
2048 = 2^11
2048^366 = 2^(11*366) = 2^4026
Now
(4^2017 = 2^4034) > (2048^366 = 2^4026) > 2018^366
Therefore
4^2017 > 2018^366
So its only logical that
4^2017 + 3^2016 > 2018^366.

answer Feb 22, 2018 by Tejas Naik



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