I've been stuck on this question.
I tried writing the number as as geometric progression plus $$2((10^{100}-1)/9)+5+5.10^2+5.10^4...$$
Got stuck in there.
2026-03-27 17:57:27.1774634247
How do i verify that $272727...2727$ ($100$ digits) can or cannot be written as a perfect square??
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Note that this is $27×1010\ldots 1$ [50 $1$s]. So $1010\ldots 1$ is not divisible by $3$. So the largest power of $3$ that divides this number is $27=3^3$ i.e., the power $3$ is odd.
ETA as noted in the comments by Stinking Bishop already