Question

☆Show that every positive even integer is not in the form of 8p+1, 8p+3, 8p+5, 8p+7!
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Answer 1

Answer:

as you can see when we multiply any number with an even number we get an even number and the next number from our even(any number) result is always odd

Step-by-step explanation:

let p=1

then 8p+1=9 and similarly for all p the result Is always odd

Answer 2

Hello, Buddy!!

To Prove:-

• Every positive even integer is not in the form of 8p+1,8p+3,8p+5,8p+7!

||Required Response||

Let, p be a Positive Natural Number.

If p is multiplied by 8, the once place digit will be 8,6,4,2,0 as according to multiples of 8.

WKT if a number is having once place of digits 2,4,6,8,0 will definitely divisible by 2. According to definition of Even Numbers, 8p will be an Even Number.

Then, 8p+1,8p+3,8p+5,8p+7,8p+9 will ends with 1,3,5,7,9 which are going to be Odd. So we can say that 8p+1,8p+3,8p+5,8p+7 are not in the form of Positive Even Number.

Simple Test:

→ 8p+1

Let, p be 2

8p+1 = 8(2)+1 = 16+1 ➝ 17

Where, 17 is a odd number

Therefore, "8p+1" is a Non Even Number.

_________________________________

→ 8p+3

Let, p be 5

8p+3 = 8(5)+3 = 40+3 ➝ 43

Where, 43 is a Odd Number

Therefore, "8p+3" is a Non Even Number.

_________________________________

→ 8p+5

Let, p be 10

8p+5 = 8(10)+5 = 80+5 ➝ 85

Where, 85 is a Odd Number

Therefore, "8p+5" is a Non Even Number.

_________________________________

→ 8p+7

Let, p be 7

87+5 = 8(7)+5 = 56+5 ➝ 63

Where, 63 is a Odd Number

Therefore, "8p+7" is a Non Even Number.

• Hence,Proved.

☆ Even Number:- Numbers which are exactly divisible by 2, are known as Even Numbers.

☆ Odd Number:- Numbers which are not divisible by 2, are known as Odd Numbers.

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Hope It Helps You ✌️