- #1
Dustinsfl
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Let p,q ∈ ℤ+ , p < q. Prove that if p - q divides p - 1, then q - p divides q - 1.
So if p - q divides p - 1, then k*(p - q) = p - 1.
Now what?
So if p - q divides p - 1, then k*(p - q) = p - 1.
Now what?
This statement is a mathematical proposition that states if the difference between two numbers, p and q, is a factor of the difference between p and 1, then the difference between q and p is also a factor of the difference between q and 1.
When we say that one number divides another, it means that the first number is a factor of the second number. In other words, the second number can be evenly divided by the first number without any remainder.
This statement is significant in mathematics because it is a conditional statement, which means that it can be used in proofs to show that one statement logically follows from another. In this case, it can be used to prove certain properties of divisibility.
Sure, for example, if we let p = 6 and q = 2, then the statement becomes "6 - 2 Divides 6 - 1 Implies 2 - 6 Divides 2 - 1". We can then see that 6 - 2 = 4, which is a factor of 6 - 1 = 5. This proves the first part of the statement. Then, 2 - 6 = -4, which is also a factor of 2 - 1 = 1. This proves the second part of the statement. Therefore, the statement is true for these values of p and q.
Yes, there are exceptions to this statement. For example, if p = 2 and q = 1, then the statement becomes "2 - 1 Divides 2 - 1 Implies 1 - 2 Divides 1 - 1". In this case, the statement is not true because 2 - 1 = 1 is not a factor of 2 - 1 = 1, and 1 - 2 = -1 is not a factor of 1 - 1 = 0. So, we cannot conclude that q - p divides q - 1 in this case.