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Decimal expansion of the square root of a nonnegative integer
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For positive integers $n$ and $k$, with $k \leq 2n$, let $\sqrt{n^2+k} = n_t \cdots n_1.a_1a_2a_3 \cdots$ be the decimal expansion of $\sqrt{n^2+k}$. In this paper, we introduce a systematic method of how to calculate the value of $a_i$ for all $i =1, 2, \dots$.
Abstract
For positive integers $n$ and $k$, with $k \leq 2n$, let $\sqrt{n^2+k} = n_t \cdots n_1.a_1a_2a_3 \cdots$ be the decimal expansion of $\sqrt{n^2+k}$. In this paper, we introduce a systematic method of how to calculate the value of $a_i$ for all $i =1, 2, \dots$.
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