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Given the Equation, Find the Solution (Posted on 2024-07-05)

Find all pairs (x, y) of positive integers that satisfy this equation:
(y+1)^y = 2*y^x+3y+1

*** Adapted from a problem which appeared at the 2012 Spanish Mathematical Olympiad.

No Solution Yet Submitted by K Sengupta

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Computer Solution

| Comment 1 of 3

I could not come up with an analytic way to solve this.

(3,3) was the only solution found with the program below:

---------

big = 1000

for x in range(1, big):

for y in range(1, big):

if (y+1)**y == 2*y**x + 3*y + 1:

print(x,y)

Posted by Larry on 2024-07-05 14:09:39

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