 #include <stdio.h>

typedef struct {
    int k;  
    int a;  
    int n;  
} Congruencia;

// Função para calcular o máximo divisor comum (MDC) usando o algoritmo de Euclides
int mdc(int x, int y) {
    while (x != 0) {
        int temp = x;
        x = y % x;
        y = temp;
    }
    return y;
}

int mdc_extendido(int a, int b, int *x, int *y) {
    if (b == 0) {
        *x = 1;
        *y = 0;
        return a;
    }
    int x1, y1;
    int mdc = mdc_extendido(b, a % b, &x1, &y1);
    *x = y1;
    *y = x1 - (a / b) * y1;
    return mdc;
}

int inverso_modular(int a, int m) {
    int x, y;
    int mdc = mdc_extendido(a, m, &x, &y);
    if (mdc != 1) {
        return -1; 
    }
    return (x % m + m) % m; 
}

int main(void) {
    int q_equa;  
    Congruencia equacoes[4];  

    printf("Você deseja resolver quantas equações? (Máximo de 4)\n");
    scanf("%i", &q_equa);

    if (q_equa < 2 || q_equa > 4) {
        printf("Número inválido de equações. Escolha entre 2 e 4.\n");
        return 1;
    }

    printf("Formato: kx ≡ a mod n\n");
    for (int i = 0; i < q_equa; i++) {
        printf("Digite os valores da equação %d:\n", i + 1);

        printf("Coeficiente de x (k%d): ", i + 1);
        scanf("%d", &equacoes[i].k);

        printf("Resto (a%d): ", i + 1);
        scanf("%d", &equacoes[i].a);

        printf("Módulo (n%d): ", i + 1);
        scanf("%d", &equacoes[i].n);

        if (equacoes[i].k != 1) {
            int inv = inverso_modular(equacoes[i].k, equacoes[i].n);
            if (inv == -1) {
                printf("Não foi possível calcular o inverso modular para k = %d e n = %d.\n", equacoes[i].k, equacoes[i].n);
                return 1;
            }
            equacoes[i].k = 1;
            equacoes[i].a = (equacoes[i].a * inv) % equacoes[i].n;
        }
    }

    for (int i = 0; i < q_equa; i++) {
        for (int j = i + 1; j < q_equa; j++) {
            if (mdc(equacoes[i].n, equacoes[j].n) != 1) {
                printf("Os módulos %d e %d não são coprimos. O sistema pode não ter solução única.\n", equacoes[i].n, equacoes[j].n);
                return 1;
            }
        }
    }

    printf("\nEquações finais:\n");
    for (int i = 0; i < q_equa; i++) {
        printf("x ≡ %d mod %d\n", equacoes[i].a, equacoes[i].n);
    }

    long long N = 1;
    for (int i = 0; i < q_equa; i++) {
        N *= equacoes[i].n;
    }
    printf("\nProduto dos módulos (N): %lld\n", N);

    long long N_values[4];
    int x_values[4];
    for (int i = 0; i < q_equa; i++) {
        N_values[i] = N / equacoes[i].n;
        x_values[i] = inverso_modular(N_values[i], equacoes[i].n);
        if (x_values[i] == -1) {
            printf("Não foi possível calcular o inverso modular para N%d = %lld mod %d.\n", i + 1, N_values[i], equacoes[i].n);
            return 1;
        }
        printf("N%d : %lld, x%d : %d\n", i + 1, N_values[i], i + 1, x_values[i]);
    }

    long long X = 0;
    for (int i = 0; i < q_equa; i++) {
        X += equacoes[i].a * x_values[i] * N_values[i];
    }
    X %= N;

    printf("Solução geral: x = %lld + %lldt\n", X, N);

    return 0;
}

created 11 months ago by ENZO EMIR VIANA FERRAZ

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About C

C language is one of the most popular general-purpose programming language developed by Dennis Ritchie at Bell laboratories for UNIX operating system. The initial release of C Language was in the year 1972. Most of the desktop operating systems are written in C Language.

Key features:

Structured Programming
Popular system programming language
UNIX, MySQL and Oracle are completely written in C.
Supports variety of platforms
Efficient and also handle low-level activities.
As fast as assembly language and hence used as system development language.

Syntax help

Loops

1. If-Else:

When ever you want to perform a set of operations based on a condition if-else is used.

if(conditional-expression) {
   // code
} else {
   // code
}

You can also use if-else for nested Ifs and if-else-if ladder when multiple conditions are to be performed on a single variable.

2. Switch:

Switch is an alternative to if-else-if ladder.

switch(conditional-expression) {    
case value1:    
 // code    
 break;  // optional  
case value2:    
 // code    
 break;  // optional  
...    
    
default:     
 // code to be executed when all the above cases are not matched;    
}

3. For:

For loop is used to iterate a set of statements based on a condition.

for(Initialization; Condition; Increment/decrement){  
  // code  
}

4. While:

While is also used to iterate a set of statements based on a condition. Usually while is preferred when number of iterations are not known in advance.

while(condition) {  
 // code 
}

5. Do-While:

Do-while is also used to iterate a set of statements based on a condition. It is mostly used when you need to execute the statements atleast once.

do {
  // code 
} while (condition);

Arrays

Array is a collection of similar data which is stored in continuous memory addresses. Array values can be fetched using index. Index starts from 0 to size-1.

Syntax

One dimentional Array:

data-type array-name[size];

Two dimensional array:

data-type array-name[size][size];

Functions

Function is a sub-routine which contains set of statements. Usually functions are written when multiple calls are required to same set of statements which increases re-usuability and modularity.

Two types of functions are present in C

Library Functions:

Library functions are the in-built functions which are declared in header files like printf(),scanf(),puts(),gets() etc.,

User defined functions:

User defined functions are the ones which are written by the programmer based on the requirement.

How to declare a Function

return_type function_name(parameters);

How to call a Function

function_name (parameters)

How to define a Function

return_type function_name(parameters) {  
  //code
}