Divisible by 2

Number Theory Level 2

Find $n$ , when $n+1|n^2 +1$ .

22 3 -2 4 5

2 solutions

Rajarshi Maiti
Jun 7, 2018

Since $n+1|n^2-1$ then if 2 is divisible by n+1 then $n+1|n^2+1$ like 2 is divisible by 2 and 2 is divisible by 2 therefore 4=2.2 divisible by 2. now n=-3,-2,0,1

Since $0$ does not divide $2$ , $n = -1$ is not a solution. There are thus 4 solutions which add to -4. Of the given options, -2 is the only possible value of $n$ , but since there are a total of 4 possible solutions for $n$ an answer of 4 is suitable given the ambiguity in the phrasing of the question.

Brian Charlesworth - 3 years ago

-2 is a answer because -1 is a factor 2^2+1 but 0 is not a answer, you are correct

Rajarshi Maiti - 3 years ago

Ok, I can see -2 as an answer, but since there are 4 possible values for $n$ , given the ambiguity in the phrasing of the question an answer of 4 is also suitable. Perhaps for sake of clarity the phrasing of the question could be "For which of the given options for $n$ does $n + 1 | n^{2} + 1$ "?

Brian Charlesworth - 3 years ago

Edwin Gray
Apr 30, 2019

(n + 1)|(n^2 + 2n + 1). If (n + 1)|(n^2 + 1), (n + 1)|2n. But (n + 1)}(2n + 2). if(n + 1)|2n, (n + 1)|2. Only n = -2 is viable from the choices

Divisible by 2

2 solutions

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