Suppose a is a positive integer and p is a prime/ Prove that p|a
if and only if the prime factorization of a contains p.
Can someone please show a full proof to this, thank you.
(Prime Numbers) An integer is said to be prime if it is
divisible by only 1 and itself. For example, 2, 3, 5 and 7 are
prime, but 4, 6, 8 and 9 are not. Write pseudocode and function
called isPrime that receives an integer and determines whether the
integer is prime or not. Write a test program that uses isPrime to
determine and print all the prime numbers between 1 and 1000.
Display 10 numbers per line. Twin primes...
Let p be an integer other than 0, ±1.
(a) Prove that p is prime if and only if it has the property
that whenever r and s are integers such that p = rs, then either r
= ±1 or s = ±1.
(b) Prove that p is prime if and only if it has the property
that whenever b and c are integers such that p | bc, then either p
| b or p | c.
Use the Well-Ordering Principle of the natural numbers to
prove that every positive
rational number x can be expressed as a fraction x = a/b where
a and b are postive
integers with no common factor.