How to resolve the algorithm Idoneal numbers step by step in the Action! programming language

Published on 12 May 2024 09:40 PM
#Action!

How to resolve the algorithm Idoneal numbers step by step in the Action! programming language

Table of Contents

Problem Statement

Idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime power or twice a prime power. A positive integer n is idoneal if and only if it cannot be written as ab + bc + ac for distinct positive integers a, b, and c with 0 < a < b < c. There are only 65 known iodoneal numbers and is likely that no others exist. If there are others, it has been proven that there are at most, two more, and that no others exist below 1,000,000.

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Step by Step solution about How to resolve the algorithm Idoneal numbers step by step in the Action! programming language

Source code in the action! programming language

;;; find idoneal numbers - numbers that cannot be written as ab + bc + ac
;;;                        where 0 < a < b < c
;;; there are 65 known idoneal numbers

PROC Main()
  CARD count, maxCount, n, a, b, c, ab, sum
  BYTE idoneal

  count = 0 maxCount = 65
  n = 0
  WHILE count < maxCount DO
    n  ==+ 1
    idoneal = 1
    a = 1
    WHILE ( a + 2 ) < n AND idoneal = 1 DO
      b = a + 1
      DO
        ab  = a * b
        sum = 0
        IF ab < n THEN
          c   = ( n - ab ) / ( a + b )
          sum = ab + ( c * ( b + a ) )
          IF c > b AND sum = n THEN idoneal = 0 FI
          b ==+ 1
        FI
      UNTIL sum > n OR idoneal = 0 OR ab >= n
      OD
      a ==+ 1
    OD
    IF idoneal THEN
      Put(' )
      IF n <   10 THEN Put(' ) FI
      IF n <  100 THEN Put(' ) FI
      IF n < 1000 THEN Put(' ) FI
      PrintC( n )
      count ==+ 1
      IF count MOD 13 = 0 THEN PutE() FI
    FI
  OD

RETURN

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