Problem #5
An integer is called a sibling number if its decimal representation
consists of two consecutive n-digit numbers concatenated together
(these constituent numbers are not allowed to have leading zeroes). For
example, 378379 and 215214 are sibling numbers, but 24023 and 99100 are
not (because of leading zeroes).
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Find all four-digit, six-digit, eight-digit, and ten-digit sibling numbers
that are perfect squares.
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Can you find infinite families of sibling numbers that are perfect
squares?