How to resolve the algorithm Curzon numbers step by step in the XPL0 programming language

Published on 12 May 2024 09:40 PM
#Xpl0

How to resolve the algorithm Curzon numbers step by step in the XPL0 programming language

Table of Contents

Problem Statement

A Curzon number is defined to be a positive integer n for which 2n + 1 is evenly divisible by 2 × n + 1. Generalized Curzon numbers are those where the positive integer n, using a base integer k, satisfy the condition that kn + 1 is evenly divisible by k × n + 1. Base here does not imply the radix of the counting system; rather the integer the equation is based on. All calculations should be done in base 10. Generalized Curzon numbers only exist for even base integers.

and even though it is not specifically mentioned that they are Curzon numbers:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Curzon numbers step by step in the XPL0 programming language

Source code in the xpl0 programming language

func ModPow(Base, Exp, Mod);
int  Base, Exp, Mod, Result;
[if Mod = 1 then return 0;
Result:= 1;
Base:= rem(Base/Mod);
while Exp > 0 do
    [if (Exp&1) = 1 then Result:= rem((Result*Base)/Mod);
    Base:= rem((Base*Base) / Mod);
    Exp:= Exp >> 1;
    ];
return Result;
];

func IsCurzon(N, K);
int  N, K, R;
[R:= K * N;
return ModPow(K, N, R+1) = R;
];

int K, N, Count;
[K:= 2;
Format(5, 0);
while K <= 10 do
    [Text(0, "Curzon numbers with base ");  IntOut(0, K);  CrLf(0);
    N:= 1;  Count:= 0;
    while Count < 50 do
        [if IsCurzon(N, K) then
            [RlOut(0, float(N));
            Count:= Count+1;
            if rem(Count/10) = 0 then CrLf(0);
            ];
        N:= N+1;
        ];
    K:= K+2;
    ];
]

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