Beal conjecture / conjecture de Beal. / published by https://github.com/dacr/code-examples-manager #cf918f8f-1587-4fca-b343-7ea0e5296b57/4a8944c5287e666ba6344cd0dad7298edc4a5449

math-beal-conjecture.sc

// summary : Beal conjecture / conjecture de Beal.
// keywords : scala, math, conjecture, beal, @testable
// publish : gist
// authors : David Crosson
// license : Apache NON-AI License Version 2.0 (https://raw.githubusercontent.com/non-ai-licenses/non-ai-licenses/main/NON-AI-APACHE2)
// id : cf918f8f-1587-4fca-b343-7ea0e5296b57
// created-on : 2019-08-14T14:43:09Z
// managed-by : https://github.com/dacr/code-examples-manager
// run-with : scala-cli $file

// ---------------------
//> using scala  "3.1.1"
//> using dep "org.scalatest::scalatest:3.2.10"
// ---------------------

/*
  Beal conjecture wikipedia : https://en.wikipedia.org/wiki/Beal_conjecture
*/

import org.scalatest._,flatspec._,matchers._
import math._

// a^x + b^y = c^z  x,y,z should be > 2
object Beal {
  def commonFactors(a: Long, b: Long, c: Long) = {
    val from = List(a, b, c)
    (1L to max(a, max(b, c))).filter { x => from.forall {
      _ % x == 0
    }
    }
  }

  // Take care as math.pow returns Double so precisions makes the formula wrongly works !
  // @ pow(1,3)+pow(99,8) == pow(99,8)
  // res1: Boolean = true
  def exploreUsingLong(l1: Long, l2: Long): Unit = {
    for {
      a <- 1L to l1
      b <- 1L to l1
      c <- 1L to l1
      x <- 3L to l2
      aPx = pow(a, x)
      y <- 3L to l2
      bPy = pow(b, y)
      z <- 3L to l2
      cPz = pow(c, z)
      if aPx + bPy == cPz
      cf = commonFactors(a, b, c).filterNot(_ == 1L)
      //if cf.size == 0 // if we want to find a counter example...
    } {
      println(s"""$a^$x + $b^$y = $c^$z\t\t${cf.mkString(",")}""")
    }
  }

  // no precision issue with this implementation
  def exploreUsingBigInt(l1: Int, l2: Int): Unit = {
    for {
      a <- 2 to l1
      bigA = BigInt(a)
      b <- 2 to l1
      bigB = BigInt(b)
      c <- 2 to l1
      bigC = BigInt(c)
      x <- 3 to l2
      aPx = bigA.pow(x)
      y <- 3 to l2
      bPy = bigB.pow(y)
      z <- 3 to l2
      cPz = bigC.pow(z)
      if aPx + bPy == cPz
      cf = commonFactors(a, b, c).filterNot(_ == 1L)
      //if cf.size == 0 // if we want to find a counter example...
    } {
      println(s"""$a^$x + $b^$y = $c^$z\t\t${cf.mkString(",")}""")
    }
  }
}

object BealConjectureTest extends AnyFlatSpec with should.Matchers {
  "beal conjecture path" should "work" in {
    succeed
  }
}
//BealConjectureTest.execute()

def now(): Long = System.currentTimeMillis()
def howLongFor[T](proc : () => T): (T, Long) = {
  val started = now()
  val result:T = proc()
  val duration = now() - started
  (result, duration)
}
def printHowLongFor[T](message:String)(proc : () => T):T = {
  val (result, duration) = howLongFor(proc)
  println(s"$message : $duration ms")
  result
}

printHowLongFor("Beal exploration using Long") { () =>
  Beal.exploreUsingLong(50, 8)
}
printHowLongFor("Beal exploration using BigInt") { () =>
  Beal.exploreUsingBigInt(50, 8)
}


//Beal.exploreUsingBigInt(200, 20)