Solve (III)

Algebra Level 2

What is the sum of all solutions of 3 x + 4 y = 5 z 3^x+4^y=5^z where x , y , and z x,y, \text{ and } z are positive integers.


The answer is 6.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Oct 7, 2018

This is not a solution, just a hint that the only solution here is x = y = z = 2 ⟹ x + y + z = 2 + 2 + 2 = 6 x=y=z=2 \implies x+y+z=2+2+2=6

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Pity that you exclude 0 as option, x, y, z = 0, 1, 1 is also valid...

Maurice van Peursem - 2 years, 8 months ago

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Yes, you are right but we need them greater than 0.

Hana Wehbi - 2 years, 8 months ago

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