/** Program to verify the (incorrect) Fermat's Library tweet:

    https://x.com/fermatslibrary/status/1813217704905474167

    which says:

    "This is the only solution to a² + b³ = c⁷ in positive integers
     15312283^2 + 9262^3 == 113^7"

    Augh.

    It uses the new faster sqrtNearestInteger function from the 2024-07-16
    release of Frink.
*/

for seven = 1 to 1001
{
   n = seven^7
   for three = 1 to floor[n^(1/3)]
   {
      n1 = n - three^3
      two = sqrtNearestInteger[n1]
      if n1 > 0 and two^2 == n1
         println["$two^2 + $three^3 == $seven^7"]
   }
}