Expophantine Dionential

Number Theory Level pending

Find the sum of all solutions to

5 x = 2 y + 3 z 5^x=2^y+3^z

in nonnegative integers.


The answer is 14.

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Bogdan Simeonov by Bogdan Simeonov , 21, Bulgaria

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1 solution

Tom Engelsman
May 2, 2020

There are three triplets that solve this Diophatine equation in N 0 : ( x , y , z ) = ( 1 , 1 , 1 ) ; ( 1 , 2 , 0 ) ; ( 2 , 4 , 2 ) . \mathbb{N_{0}}: (x,y,z) = (1,1,1); (1,2,0); (2,4,2). The coordinate sum computes to:

Σ n = 1 3 x n + y n + z n = 14 . \Sigma_{n=1}^{3} x_{n} + y_{n} + z_{n} = \boxed{14}.

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