Let m,n be integers. It is known that there are integers a,b such that am+bn=1 if, and only if, the greatest common divisor of m,n is 1. You are not required to prove this.Now suppose that p,q are different odd primes. In each case determine if there are integers a,b such that ap+bq=1 so that the given condition is satisfied:a. p divides b and q divides a;
b. p divides a and q divides b;
c. p does not divide a and q does not divide b.
number theorygreatest common divisornumber theory unsolved