It is given that 5 does not divide n - 1, n and n + 1, where n is a positive integer. Which one of the following is correct ?

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CDS Elementary Mathematics 16 April 2023 Official Paper

Answer 1

Concept:

Divisibility rule of 5: A number is divisible by 5 only if the unit digit is 0 or 5.

Calculation:

Let n - 1, n & n + 1 be 6, 7 & 8.

⇒ n² + 1 = 7² + 1 = 50

⇒ n2 - 1 = 72 - 1 = 48

⇒ n2 + n = 72 + 7 = 56

⇒ n2 - 7 = 72 - 7 = 42

∴ 5 divides n² + 1

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