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 positive integer.​

Answer 1

n + 12 = 5 q + 3 + 12 = 5 q + 15 , which is divisible by 5. ... n + 12 = 5 q + 4 + 12 = 5 q + 16 , which is not divisible by 5. n + 16 = 5 q + 4 + 16 = 5 q + 20 , which is divisible by 5. Hence, in each case, only one out of n , n + 4 , n + 8 , n + 12 and is divisible by 5.

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