Question

Is a square of an even number always even? In 1.2 you wrote the general term of sequences you wrote in 1.1.1-1.1.3 If a number is even, it can always be written as 2x another number Eg: 28 = 2 x 14 In symbols we write this as 2 x nor 2n Do you agree with the statement below? "A square of an even number is always even". Explain your answer

Answer 1

5)

5.1

Given equation is

`P=n^2-n+41`

Replace n=1, we get

`P=1-1+41=41`

We know that a number divisible by one and itself is called a prime number.

Here 41 is divisible by 1 and 41 only.

Hence 41 is a prime number.

5.2.

Substitute n=37 in the equation of P, we get

`P=(37)^2-37+41`

`P=1369-37+41`

`P=1373`

The number 1373 is divisible by one and 1373 only.

So 1373 is a prime number.

Hence if n=37, then P is a prime number.

5.3.

We need to choose three numbers greater than 38.

Let n=39 and substitute in P, we get

`P=(39)^2-39+41`

`P=1521-39+41`

`P=1523`

The number 1523 is divisible by one and 1523.

Hence 1523 is a prime number.

Let n=40 and substitute in P, we get

`P=(40)^2-40+41`

`P=1600-40+41`
`P=1601`

The number 1601 is divisible by one and 1601.

Hence 1601 is a prime number.

Let n=41 and substitute in P, we get

`P=(41)^2-41+41`
`P=1681-41+41`

`P=1681`

The number 1681 is divisible by one and 1681.

Hence 1681 is a prime number.

We get that

When n=39,40 and 41 then P is prime.

5.4)

Yes, I believe that this conjecture is true.

we have chosen n=1, n=39 0dd number, n=40 even number, and n=41 prime number then we get the prime number for P.

So this conjectures is true for any value of n.

The equation P gives the prime number.