MHB Solving equation in natural number

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The equation presented is 144 + 144^49 + 144^(49^2) + ... + 144^(49^2018) = 3(y^4038 - 1), where y must be an odd natural number. The original poster expresses excitement about making progress but finds the rewritten form unhelpful. There is a sense of determination to solve the equation despite the challenges. The discussion highlights the complexity of finding the natural number y that satisfies the equation. The pursuit of a solution continues, indicating ongoing engagement with the problem.
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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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