Sage-Tips

How do you prove that N 5 is divisible by 5?

So for the square of any number the last digits can only be 0,1,4,5,6,9. Thus n^5–n is always divisible by 5, as the last digit of squares of any number is either equal to 0 or 5, or it differs from 0 and 5 by 1, ie it is 1 or 9 in case if 0 and 4 or 6 in case of 5.

Can you give an example of a number which is divisible by 6 but not by 2 and 3?

Answer: No there is not any number which is divisible by 6 but not 2 and 3. The number which is divisible by 2 and 3 only that is divisible by 6.

How do you know something is divisible by 5?

A number is divisible by 5 if the number’s last digit is either 0 or 5. Divisibility by 5 – examples: The numbers 105, 275, 315, 420, 945, 760 can be divided by 5 evenly. The numbers 151, 246, 879, 1404 are not evenly divisible by 5.

How do you know if a number is divisible by another number?

A number is divisible by another number if it can be divided equally by that number; that is, if it yields a whole number when divided by that number. For example, 6 is divisible by 3 (we say “3 divides 6”) because 6/3 = 2, and 2 is a whole number.

How do you know if something is divisible by 5?

Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5. If the last digit in the number is 0, then the result will be the remaining digits multiplied by 2.

Which of the following number is divisible by 6 answer?

A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156. [We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].

Is 6 N – 1 always divisible by 5?

Prove 6 n − 1 is always divisible by 5 for n ≥ 1. Base Case: n = 1: 6 1 − 1 = 5, which is divisible by 5 so TRUE. Assume true for n = k, where k ≥ 1 : 6 k − 1 = 5 P.

What number minus 1 is divisible by 5?

6 has a nice property that when raised to any positive integer power, the result will have 6 as its last digit. Therefore, that number minus 1 is going to have 5 as its last digit and thus be divisible by 5. Thanks for contributing an answer to Mathematics Stack Exchange!

What is the remainder of 6K after division by 5?

We can show by induction that 6 k has remainder 1 after division by 5. The base case k = 1 (or k = 0) is straightforward, since 6 = 5 ⋅ 1 + 1. Now suppose that 6 k has remainder 1 after division by 5 for k ≥ 1. Thus 6 k = 5 ⋅ m + 1 for some m ∈ N. We can then see that = 5 ( 5 ⋅ m + m + 1) + 1. Thus 6 k + 1 has remainder 1 after division by 5.

Is n(n + 1) (n + 5) a multiple of 3?

Ex 4.1, 19 – Prove: n (n + 1) (n + 5) is a multiple of 3 Ex 4.1,19 Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3.