Question

show that one and only one out of n, n+4,n+8,n+12,and n+16 is divisible by 5, where n is any whole number
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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,thenn=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=

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