How to resolve the algorithm Idoneal numbers step by step in the ALGOL 68 programming language

Published on 12 May 2024 09:40 PM
#Algol 68

How to resolve the algorithm Idoneal numbers step by step in the ALGOL 68 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 ALGOL 68 programming language

Source code in the algol programming language

BEGIN # find idoneal numbers - numbers that cannot be written as ab + bc + ac #
      #                        where 0 < a < b < c                            #
      # there are 65 known idoneal numbers                                    #
    INT count    :=  0;
    INT max count = 65;
    FOR n WHILE count < max count DO
        BOOL idoneal := TRUE;
        FOR a TO n - 2 WHILE idoneal DO
            FOR b FROM a + 1 TO n - 1
            WHILE INT ab = a * b;
                  INT c   = ( n - ab ) OVER ( a + b );
                  INT sum = ab + ( c * ( b + a ) );
                  sum <= n
              AND ( idoneal := c <= b OR sum /= n )
            DO SKIP OD
        OD;
        IF idoneal THEN
            print( ( " ", whole( n, -4 ) ) );
            IF ( count +:= 1 ) MOD 13 = 0 THEN print( ( newline ) ) FI
        FI
    OD
END

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