Question

Please help me answer, the last answer was incorrect.

We want to prove that 119 has infinitely many multiplicative inverses modulo 198. (a) Prove that such a multiplicative inverse exists. (b) Verify that 5 is one of them. (c) Prove that there are infinitely many inverses. Hint: Consider the number (5 + n · 198) (d) Generalize the statement: Try to prove that for any two positive integers a and b that are relative primes, there are infinitely many multiplicative inverses of a modulo b.

Answer 1

/*

Function: uppercaseMethod

Purpose: Converts all lower case letters found within the line to uppercase

*/

void * uppercaseMethod(void *arg)

{

int i;

for(i = 0; i < 63; i++)

{

if(islower(input[i]))

{

input[i] = toupper(input[i]);

}

}

}

/*

Function: writeMethod

Purpose: Writes formatted line to screen and file

*/

void * writeMethod(void *arg)

{

int m;

char e, d;

Queue obj;

if(input != " ")

{

for(m = 0; m < input.length(); m++)

{

e = input[m];

obj.Enqueue(e);

}

for(m = 0; m < input.length(); m++)

{

d=obj.Dequeue(d);

}

cout << " Line " << lineNum << ": ";

cout << input << endl;

outFile << input << endl;

lineNum++;

}

}

/*

Function: readerMethod

Purpose: Reads each line from file

*/

void * readerMethod(void *arg)

{

ifstream infile("file.txt");

cout << "The file is now opened!" << endl;

cout << "\nReading input file now..." << endl;

cout <<" _________________________________\n" << endl;

for(m = 0; m < input.length(); m++)

{

e = input[m];

obj.Enqueue(e);

}

for(m = 0; m < input.length(); m++)

{

d = obj.Dequeue(d);

cout << " Line " << lineNum << " : ";

cout << input << endl;

outFile << input << endl;

lineNum++;

}

/*

Function: readerMethod

Purpose: Reads each line from file

*/

void * readerMethod(void *arg)

{

ifstream inFile("file.txt");

cout << "The file is now opened!" << endl;

cout << "\nReading input file now..." << endl;

cout <<" _________________________________\n" << endl;

while(!inFile.eof())

{

getline(inFile, input);

int i;

for(i = 0; i < input.length(); i++)

{

if(i >= 63)

{

string j;

j = "";

input[i] = j[0];

}

}

symbolMethod(NULL);

uppercaseMethod(NULL);

writeMethod(NULL);

}

inFile.close();

outFile.close();

return NULL;

}

pthread_mutex_t mutex1 = PTHREAD_MUTEX_INITIALIZER;

int main(int argc, char **argv)

{

int argc, char **argv

pthread_t reader, munch1, munch2, writer; //Create the four threads

pthread_mutex_lock(&mutex1);

// produces error messages when a thread cannot be created

if(pthread_create(&reader, NULL, readerMethod, Null))

{

cout << "\n!!Reader Thread could not be created!!\n;

return -1;

}

pthread_mutex_unlock(&mutex1);

else if(pthread_create(&munch1, NULL, symbolMethod, NULL))

{

cout << "\n!!Reader Thread could not be created!!\n;

return -1;

}

else if(pthread_create(&munch2, NULL, uppercaseMethod, NULL))

{

cout << "\n!!Reader Thread could not be created!!\n;

return -1;

}

else if(pthread_create(&writer, NULL, writeMethod, NULL))

{

cout << "\n!!Reader Thread could not be created!!\n;

return -1;

}

//Produces error messages when a thread cannot be joined

if(pthread_join(reader, NULL)

{

cout << "\n!!Could not join thread!!\n";

}

else if(pthread_join(munch1, NULL))

{

cout << "\n!!Could not join thread!!\n;

return -1;

}

else if(pthread_join(munch2, NULL))

{

cout << "\n!!Could not join thread!!\n;

return -1;

}

else if(pthread_join(writer, NULL))

{

cout << "\n!!Could not join thread!!\n;

return -1;

}

cout << "\nThe file contains " << lineNum-1 << "line(s) of input.\n";

cout << "----------------------------------------------------\n" << endl;

return 0;

}