Algebra question #1

Number Theory Level 4

If ( x + 5 ) 3 + ( x + 7 ) 3 = ( 3 x + 1 ) 3 (x + 5)^{3} + (x + 7)^{3} = (3x + 1)^{3} . How many positive integers "x" that satisfy this equation.

Algebra Question


The answer is 0.

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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2 solutions

Paul Ryan Longhas
Nov 13, 2014

Since x is positive integer, so x + 5 is also positive integer at the same manner x + 7 and 3x + 1 is also a positive integers. So, no positive integers x that satisfy this equation by Fermat's Last Theorem.

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T O P A U L R Y A N L O N G H A S TO PAUL RYAN LONGHAS : Salute to you bro,........................... what a great aplication. Anyone first would only think of solving it

Abhisek Mohanty - 5 years, 10 months ago
Pablo Padilla
Dec 7, 2015

Fermat's last theorem (recently proven) states that no integers x,y,z satysfy an equation of the form x n + y n = z n x^{n}+y^{n}=z^{n} if n is greater than 2. The present equation is just a particular case of this theorem.

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