The positive integers
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
and
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
are such that the numbers
![15a + 16b](/media/m/a/2/5/a25c12223bea0511140ff92b259ee12b.png)
and
![16a - 15b](/media/m/6/7/a/67a332e17da6597abff8f5d7c78549db.png)
are both squares of positive integers. What is the least possible value that can be taken on by the smaller of these two squares?
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The positive integers $a$ and $b$ are such that the numbers $15a + 16b$ and $16a - 15b$ are both squares of positive integers. What is the least possible value that can be taken on by the smaller of these two squares?