Solving equation in natural number

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SUMMARY

The discussion centers on solving the equation \( 144 + 144^{49} + 144^{49^2} + 144^{49^3} + \ldots + 144^{49^{2018}} = 3(y^{4038} - 1) \) for natural number \( y \), specifically requiring \( y \) to be an odd number. Participants express their challenges in simplifying the equation and finding a solution. The equation involves exponential growth and requires a deep understanding of number theory to derive \( y \) effectively.

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  • Understanding of natural numbers and their properties
  • Familiarity with exponential equations and series
  • Basic knowledge of number theory
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  • Learn about modular arithmetic and its applications in solving equations
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Mathematicians, students studying number theory, and anyone interested in solving complex equations involving natural numbers and exponentials.

anemone
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What is the natural $y$ from $144+{{144}^{49}}+{{144}^{{{49}^{2}}}}+{{144}^{{{49}^{3}}}}+...+{{144}^{{{49}^{2018}}}}=3({{y}^{4038}}-1)$?
 
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y must be an odd number. Yippee! I got somewhere with it! (Sun)

I rewrote it into (what I think is) a simpler form but it tells me nothing. I'm going to be up all night trying to grok this one.

-Dan
 

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