Please solve the following functions using Scala!

 object arithmetic { def sqrt(n: Int): Option[Int] = { // = None if n  1 } def gcd(n: Int, m: Int): Option[Int] = { // = None if n or m  
 
 
 
 
object testArith extends App { println("gcd(15, 12) = " + arithmetic.gcd(15, 12)) println("lcm(15, 12) = " + arithmetic.lcm(15, 12)) println("gcd(13, 12) = " + arithmetic.gcd(13, 12)) println("gcd(-13, 12) = " + arithmetic.gcd(-13, 12)) println("phi(9)= " + arithmetic.phi(9)) println("sqrt(49) = " + arithmetic.sqrt(49)) println("sqrt(37) = " + arithmetic.sqrt(37)) println("sqrt(35) = " + arithmetic.sqrt(35)) println("log(64) = " + arithmetic.log(64)) println("log(130) = " + arithmetic.log(130)) println("log(9) = " + arithmetic.log(9)) println("log(0) = " + arithmetic.log(0)) println("isPrime(23) = " + arithmetic.isPrime(23)) println("isPrime(59) = " + arithmetic.isPrime(59)) println("isPrime(75) = " + arithmetic.isPrime(75)) }
 
 
  If Mathematics is the queen of the sciences, then Number Theory (aka arithmetic) is the queen of mathematics. Number theory studies the natural numbers (aka the unsigned integers: 0, 1, 2, 3, ...). The focus of number theory is on division and remainders. Complete the implementation of arithmetic.scala. Test it with the app arithTest.scala. Here's the expected output: god (15, 12) = Some (3) lcm (15, 12) Some (60) gcd (13, 12) Some (1) gcd (-13, 12) = None phi (9) = Some (6) sqrt (49) Some (7) sqrt (37) Some (6) sqrt (35) Some (5) log (64) Some (6) log (130) Some (7) log (9) Some (3) log (0) None isPrime (23) = Some (true) isPrime (59) = Some (true) isPrime (75) = Some (false) = = =  If Mathematics is the queen of the sciences, then Number Theory (aka arithmetic) is the queen of mathematics. Number theory studies the natural numbers (aka the unsigned integers: 0, 1, 2, 3, ...). The focus of number theory is on division and remainders. Complete the implementation of arithmetic.scala. Test it with the app arithTest.scala. Here's the expected output: god (15, 12) = Some (3) lcm (15, 12) Some (60) gcd (13, 12) Some (1) gcd (-13, 12) = None phi (9) = Some (6) sqrt (49) Some (7) sqrt (37) Some (6) sqrt (35) Some (5) log (64) Some (6) log (130) Some (7) log (9) Some (3) log (0) None isPrime (23) = Some (true) isPrime (59) = Some (true) isPrime (75) = Some (false) = = =