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Question 5
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 positive integer


Solution

Given numbers are n, (n + 4), (n + 8), (n + 12) and (n + 16), where n is any positive integer
Then, let n = 5q, 5q + 1, 5q + 2, 5q + 3, 5q + 4 for q ϵ  N
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.


Mathematics

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