Mathematics 301-002 Fall 2017 and p is a positive prime number. The predicate is
ID: 3148802 • Letter: M
Question
Mathematics 301-002 Fall 2017 and p is a positive prime number. The predicate is this: ab mod p = (ab mod p) mod p For instance, if we have a = 3 , 4 , and p = 2 , then 6. We are going to 34 mod 2 = 81 mod 2 = 1 and (34 mod 2) mod 2 = 30 mod 2 = 1 So the statement P(3,4,2) is True. Okay, now you know what P is. Here is the question: Is the statement P(a,b, p) true for all positive integers a and b and all primes p ment is alpays true, you should provide a proof. If the statement is not always true, you should provide a counterexample. 7. Let f be the function defined on (some) real numbers as follows: 3x -1 Is the function one-to-one? Make sure to explain your answer.Explanation / Answer
Here is a counter example:
a= 2; b=5 and p=3;
Here 'a' and 'b' are positive numbers and p=3 is a prime number;
ab mod p = 25 mod 3 = 32 mod 3 = 2;
(ab mod p) mod p = (2 5 mod 3 ) mod3 = (22) mod 3 = 4 mod 3 = 1
In this counter example we see that :
(ab) mod p is not equal to (ab mod p) mod p