The discussion clarifies the definition of prime numbers, stating that an integer n is prime if n > 1 and for all positive integers r and s, if n = (r)(s), then either r = 1 or s = 1. The confusion arises from the incorrect assertion that if n = (r)(s), then r > 1 or s > 1, which is not universally applicable. The correct interpretation emphasizes that prime numbers have no factors other than 1 and themselves, reinforcing the uniqueness of their factors.
PREREQUISITESMathematicians, educators, students of mathematics, and anyone interested in the foundational concepts of prime numbers and their properties.
What? No! if 6= (r)(s) then either r= 3 and s= 2 or r= 2 and s= 3 or r= 1 and s= 6 or r= 6 and r= 1. "If n= (r)(s), then r> 1 or s> 1" is true for all positive integers except 1.jonroberts74 said:An integer is prime if, and only if, n > 1 and for all positive integers r and s, if
n = (r)(s), then r > 1 or s > 1.
This is now true for all positive integers. What is true for prime numbers only is "If n= (r)(s) then r= 1 or s= 1."It should be if n = rs, then r great than or equal 1 or s greater than or equal 1
correct?