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A multi-solution diophantine problem (Posted on 2006-09-15)

Consider the equation x^2+y^5=z^3 where x, y, and z, are positive integers.

(A) Can you give at least three solutions to it?
(B) Determine whether or not there is an infinite number of solutions.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Many solutions (all of them?)

| Comment 1 of 7

If x=2^5P and y=2^2P, the left hand side of the equation is 2^(10P+1), so 10P+1 must be a multiple of 3. Letting P=3K+2, 10P+1 becomes 30K+21, so x=2^(15K+10), y=2^(6K+4), z=2^(10K+7) is a solution for all K.

Posted by Old Original Oskar! on 2006-09-15 11:49:40

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