No. It's not true for n=2, where 14n - 1 = 28 - 1 = 27, which is not
This statement is true when the two integers are positive, or when the two integers are negative.
That is false. This type of statement is only true for prime numbers, not for compound numbers such as 6. Counterexample: 2 x 3 = 6
Mathematical induction is just a way of proving a statement to be true for all positive integers: prove the statement to be true about 1; then assume it to be true for a generic integer x, and prove it to be true for x + 1; it therefore must be true for all positive integers.
The statement cannot be proven because it is FALSE. If one of x and y is odd and the other is even then x2 + y2 MUST be odd. Also if x and y are even then x2 + y2 MUST be divisible by 4. The statement is only true if x and y are odd integers. Whether or not they are positive makes little difference.
That's a true statement. Another true statement is: All integers are rational numbers.
There does not exist a number that is divisible by all integers. The opposite is true. The number one can divided into all integers.
It is not true.
They are integers.
No, integers can be positive or negative.
No, integers are positive and negative whole numbers
False - if the sentence is meant to be exhaustive. Integers can be positive or negative OR ZERO.
It is a statement which is true for some sums.
126 is divisible by 6 and 9
If a conditional statement is true then its contra-positive is also true.
This statement is true because 1 is a factor of any 2 positive integers and so is always a common factor and since it is the smallest or lowest positive integer, it is always the lowest common factor.
No, that is not true.
yes always this is true' example 1,2,3 sum is 6 and is divisible by 3
It is a TRUE statement.
noIt is true that if a number is divisible by 6, it alsodivisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6.http://wiki.answers.com/A_number_is_divisible_by_6_if_and_only_if_it_is_divisible_by_3&action=edit
They are positive integers with only two factors.
Negation is the opposite of something actual or positive. The negation of a true statement will be false. The negation of a false statement will be true.
That is a true statement.