The Two Strange Numbers
Number Theory
Level
pending
There are two distinct positive integers: the difference of their squares is a cube and the difference of their cubes is a square, and their product is minimal. What is the product of these two integers?
The answer is 60.
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1 solution
Mathematica
FindInstance[a^2-b^2==x^3&&a^3-b^3==y^2&&a>b>0,{a, b, x, y},Integers]{{a -> 10, b -> 6, x -> 4, y -> -28}}