$\underline{\text { Folkpor }}$

It is known that the expressions $4 k+5$ and $9 k+4$ for some natural values of $k$ are simultaneously perfect squares. What values can the expression $7 k+4$ take for the same values of $k$?
Let $4 k+5=m^{2}$ and $9 k+4=n^{2}$, where $m$ and $n$ are some natural numbers. Then $9 m^{2}-4 n^{2}=29=(3 m-2 n)(3 m + 2 n)$.

Thus, $3 m-2 n=1, 3 m+2 n=29$, from which $m=5, n=7, k=5$, and $7 k+4=39$.

## Answer

39.

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