perplexus.info :: Just Math : A simple equation

A simple equation (Posted on 2018-06-24)

Solve (pen and paper only):

5*3^x+4=y²

List all possible integer solutions.

No Solution Yet Submitted by Ady TZIDON

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| Comment 1 of 3

a few very small steps:

clearly x is not negative else the LHS is not integer.

x = 0 and y= +/- 3 is a solution.

for all y that work, so does -y, as LHS is positive

x are even, since this produces LHS numbers ending in ..09 and ...49

(x odd makes numbers ending in 19 and 39 which can not be squares)

likewise y ends in 3 or 7

I wonder how 5*3^x=(y-2)(y+2) might help

Edited on October 10, 2018, 5:24 pm

Posted by Steven Lord on 2018-06-24 15:11:46

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