Question

Example 4. Show that one and only one out of
nn +4, n +8, n +12 and n +16 is divisible by 5.
where n is any positive integers
$plz \: answer \: me \: fast$
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Answer 1

Step-by-step explanation:

Consider the positive integer is of the form

5q, 5q+1 ,5q+2 ,5q+3.....

Here

b=5

r=0,1,2,3,4,

Where r=0. =n=5q

Now, n=5q is divisible by 5

n+4=5q+4. {not divisible by 5}

n+8=5q+8. {not divisible by 5}

n+6=5q+6. {not divisible by 5}

n+12=5q+12. {not divisible by 5}

Where r=1, n=5q+1

n=5q+1

n+4=5q+5. {divisible by 5}

n+8=5q+9. {not divisible by 5}

n+6=5q+7 {not divisible by 5}

n+12=5q+13. {not divisible by 5}

Where r=2, n=5q+2

n=5q+2

n+4=5q+6 {not divisible by 5}

n+8=5q+10 {divisible by 5}

n+6=5q+8. {not divisible by 5}

n+12=5q+14 {not divisible by 5}

Where r=3, n=5q+3

n=5q+3

n+4=5q+7. {not divisible by 5}

n+8=5q+11 {not divisible by 5}

n+6=5q+9 {not divisible by 5}

n+12=5q+15. { divisible by 5}

When,

r=4, n=5q+4

n=5q+4

ln+4=5q+8. {not divisible by 5}

n+8=5q+12 {not divisible by 5}

n+6=5q+10. { divisible by 5}

n+12=5q+16. {not divisible by 5}

From 1, 2, 3, 4, 5 Its clear that, one and only one out of n,n+4,n+12,n+6 is divisible by 5

Hence, this is the answer.

......I tried .......

......dark lover......

Answer 2

Answer:

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