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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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