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Find one possible pair of values for x and y. If x,y and x-y are two-digit numbers. x is a square number, y is a cube number and x-y is a prime number.

Is it as easy as I am thinking it is? Or I am trying to complicate things by looking for the equations here.

The simplest way I can see is to write down all these two-digit numbers and then choose on possible option.

But, is it??

laila
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1 Answers1

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Yes, there is probably no easy "elegant math" way to do this, and there are only 9 square numbers and 4 cube numbers that are two digit (if you allow including a leading zero, otherwise there are even fewer). You can further limit the search by noting that unless you can get $x - y = 2$, then either $x$ is odd and $y$ is even or vice versa.

user2566092
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  • If you exclude leading zeros and negative numbers, you are left with checking which of $36-27$, $64-27$ and $81-64$ are prime. Two are and you only need one. – Henry Feb 02 '15 at 22:43