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Some Quartic Expressions Sum to Fourth Powers (Posted on 2023-07-04)

Find all possible sextuplets (x,y,z,p,q,r) of positive integers that satisfy this system of equations:

x⁴+14xy+1 = p⁴
y⁴+14yz+1 = q⁴
z⁴+14xz+1 = r⁴

Prove that there are no further valid sextuplets satsfying the given conditions.

Notes:
• Adapted from a problem appearing in Soros Math Olympiad.
• Computer program assisted solutions are welcome, but a semi-analytic solution is preferred.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(x,y,z,p,q,r)= (1,1,1,2,2,2)
For an explanation refer to the solution submitted by Brian Smith in this location.
.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Analytic Solution	Brian Smith	2023-07-04 11:17:49
solution	Charlie	2023-07-04 08:32:33

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