Find all integer numbers n such that 11 n − 5 n + 4 is a perfect square.Find all integer numbers n, such that, 11 n − 5 n + 4 ∈ N I really tried but I couldn't guys, help please.

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Find all integer numbers n such that             11      n      −      5              n      +      4       is a perfect square.Find all integer numbers n, such that,                     11        n        −        5                    n        +        4              ∈      N  I really tried but I couldn&#039;t guys, help please.

tilsjaskak6 · Accepted Answer

If our square root is to be an integer, we need to have             11      n      −      5              n      +      4       a non-negative integer. Note that            11      n      −      5              n      +      4        =  11  −      49          n      +      4        .So   n  +  4 must divide   49.  But    49  has very few divisors, so there are very few possile integer values of       49          n      +      4      . Try them all, including the negative ones. For each candidate, check whether the number   11  −      49          n      +      4       is a perfect square.

pablos28spainzd · Accepted Answer

hint:                     11        n        −        5                    n        +        4              =      k    2    →  11  n  −  5  =  n      k    2    +  4      k    2    →  n  (  11  −      k    2    )  =  5  +  4      k    2    =  49  +  4  (      k    2    −  11  )  →  n  =                    −        49                              k          2                −        11              −  4  →      k    2    −  11  =  ±  1  ,  ±  7  ,  ±  49.From this you can find all possible values of k, and then find n.

Find all integer numbers n such that 11 n −

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