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GCD problem

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Source: — Data Sufficiency |
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by pepeprepa » Mon Aug 25, 2008 9:41 am
You can try a little if like me you don't find it obvious:
20 and 21
1 and 2
15 and 14
19 and 18
1 and 0

It seems that 2 consecutive positive integers have 1 as greatest factor. Try to take several examples to be sure there is not an exception.
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by Ian Stewart » Mon Aug 25, 2008 12:16 pm
Yes, the GCD of two consecutive positive integers is always 1. Say x and x+1 are consecutive positive integers, and say d is a divisor of x. That is, x is a multiple of d. Then the nearest multiples of d to x are x+d and x-d; x+1 can't be divisible by d if d > 1. So if d is a divisor of x, d is never a divisor of x+1, unless d is equal to 1.
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