2019年12月31日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2013年5月20日 · Many years ago, I noticed that $987654321/123456789 = 8.0000000729\\ldots$. I sent it in to Martin Gardner at Scientific American and he published it in his column!!! My life has gone downhill si...

$\begingroup$ The possible tests you can use for proving something is not a square is more than just modulo3 and modulo 4 tests., you could do for example a modulo 10 test: The possible final digits for square numbers are $0,1,4,5,6,9$ so if the final digit happens to be a $2,3,7,8$ we know immediately that it cannot be a square.

2017年5月7日 · I just started typing some numbers in my calculator and accidentally realized that $\\frac{123456789}{987654321}=1/8$ and vice versa $\\frac{987654321}{123456789}=8.000000072900001$, so very close to...

2017年1月20日 · Consider the product. $$9\cdot123456789=1111111101.$$ This pattern is due to the fact that $9$ is one less than the basis of the numeration so that the products with individual digits (from the right $81,72,63,54\cdots$) have an …

R. J. Cano (in private email communications with me) expressed his intuitive prediction that in the base 10 more pairs (he generously named them PovolotskyPairs) of such permutations could be found, that is such pairs of distinct digits permutations, which yield the very same ratio 109739369/13717421 = 8.0000000729... .

2014年12月28日 · I got this remarkable thing when I divided $16$ by $162$, or, in a simplified version, $8$ by $81$. It's $0.098765432098765432\\cdots$, or more commonly known as $0.\\overline{098765432}$, with all ...

Here is another way to do this. Consider the polynomial $$\begin{align}&P(x)=\sum^{n-1}_{i=0} \ i\ \cdot \ x^i= 0x^0 +1x^1+2x^2+3x^3+\cdots +(n-1)\ x^{n-1}\\&Q(x ...

After playing with my calculator for a while I tried doing $\\frac{9876543210}{0123456789}$ and it came out as $80.000000729$ which came really close to a whole number so I tried it for the first 16

2014年9月4日 · I agree with the above responses regarding part a. The correct answer to part (a) is 9/499. We want to find the probability of choosing a second defective item, after selecting a defective item.