perplexus.info :: Numbers : Add 100 to Cube, Get Square

Add 100 to Cube, Get Square (Posted on 2023-07-13)

Each of x and y is a positive integer.

Determine the minimum value of x+y such that:

       x³ + 100 = y²

What are the next two smallest values of x+y in consonance with the given conditions?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Possible Solution

Comment 2 of 2 |

One possible way is to obxerve that x^3 can be a difference of squares

such that x =(y-10), x^2 = (y+10).

Then x(x-1)=20, so x=5, and checking, 125+100=225 or (x+10) or 15^2.

Posted by broll on 2023-07-14 06:23:31

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