Question by Summer Clouds - Discuss with MathYouLike

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10/10/2017 at 08:50

Prove that $a$ and $a+1$ have no any common divisor (without $1$ , of course)?

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Phan Thanh Tinh Coordinator 10/10/2017 at 10:34

Let d be the common divisor of a and a + 1 (\(d\in Z^+\)), then a and a + 1 are divisible by d. So, (a + 1) - a = 1 is also divisible by d

\(\Rightarrow d=1\)

Hence, a and a + 1 are relatively prime numbers
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