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Task/Totient-function/S-BASIC/totient-function.basic

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+$lines
+
+rem - return p mod q
+function mod(p, q = integer) = integer
+end = p - q * (p / q)
+
+rem - return greatest common divisor of x and y
+function gcd(x, y = integer) = integer
+   var r, temp = integer
+   if x < y then
+      begin
+         temp = x
+         x = y
+         y = temp
+      end
+   r = mod(x, y)
+   while r <> 0 do
+      begin
+         x = y
+         y = r
+         r = mod(x, y)
+      end
+end = y
+
+rem - return phi (also called totient) of n
+function phi(n = integer) = integer
+   var i, count = integer
+   count = 1
+   for i = 2 to n
+      if gcd(n, i) = 1 then count = count + 1
+   next i
+end = count
+
+rem - exercise the function
+var n, totient, count = integer
+print "  n    Phi(n)   Prime?"
+for n = 1 to 25
+   totient = phi(n)
+   print using "####  ####     ";n, totient;
+   if totient + 1 = n then
+      print "yes"
+   else
+      print "no"
+next n
+
+rem - and further test it by counting primes
+print
+count = 0
+for n = 1 to 1000
+   if phi(n) = n - 1 then count = count + 1
+   if n = 100 then
+      print "Primes up to 100  = ";count
+   else if n = 1000 then
+      print "Primes up to 1000 = ";count
+next n
+
+end