Question

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Show that one and only one out of n, n +4, n + 8, n + 12 and n + 16 is divisible by 5 wher
n is any positive integer.​

Answer 1

Answer:

Given numbers are n, (n+ 4), (n + 8), (n + 12) and (n + 16), where n is any positive integer.

Then, let n = 5q, 5g + 1, 5g + 2, 5g + 3, 5q + 4 for q∈ N [by Euclid’s algorithm]

Then, in each case if we put the different values of n in the given numbers. We definitely get one and only one of given numbers is divisible by 5.

Hence, one and only one out of n, n+ 4, n+ 8, n+12 and n+16 is divisible by 5.

Alternate Method

On dividing on n by 5, letq be the quotient and r be the remainder.

Then =5q + r, where 0<r< 5.

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