Chain of divisibilities

Number Theory Level 4

Find the largest integer $n$ such that:

If $n, n+1, n+2$ divide an integer $k$ , then $n+3$ also divides $k$ .

The answer is 3.

1 solution

Achal Jain
May 11, 2017

[This is not a solution.]

Isn't the answer wrong?

I can have multiple values of $Y$ if I put $X=1(\text{which is the only solution to the problem)}$ then i can have any positive integral values for $Y$ .

[ I've updated this comment ]

Sorry, you're absolutely right. I've fixed it.

Pi Han Goh - 4 years, 1 month ago

I think you want Y to be greater than 1.

The only possible solution is for X = 1 (or -1).

Calvin Lin Staff - 4 years, 1 month ago

Sorry, I mistook "divides" by "is divisible by". I've fixed the question (again). Thanks for pointing it out~!

Pi Han Goh - 4 years ago

@Pi Han Goh – I've fixed it again....

Pi Han Goh - 4 years ago

why not Y=2 and X=60 ?

Kushal Bose - 4 years ago

I think you mean x=2 and y=60, but yes, that would work.

Siva Budaraju - 4 years ago

But y,y+1,y+2 should divides X.but 60,61,62 doe not divide X

Kushal Bose - 4 years ago

@Kushal Bose – Oh, sorry. I mixed up y and x.

Siva Budaraju - 4 years ago

Thanks. I've updated the answer to 2. Those who previously answered 2 has been marked correct.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the “line line line” menu in the bottom right corner. This will notify the problem creator who can fix the issues.

Brilliant Mathematics Staff - 4 years ago

I have fixed the problem. The issue was with the lack of clarity about which variable is variable, and when.

Calvin Lin Staff - 4 years ago

Chain of divisibilities

The answer is 3.

1 solution

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