Wikipedia:Reference desk/Archives/Mathematics/2019 April 1

= April 1 =

Find three integers $$n_1, n_2, n_3$$ such that $$n_1^3 + n_2^3 + n_3^3 = 42$$
I tried to find a solution to $$n_1^3 + n_2^3 + n_3^3 = 42$$ for $$n_1,n_2,n_3\in \mathbb{Z}$$ using a computer program, but so far I haven't found a solution. Count Iblis (talk) 03:37, 1 April 2019 (UTC)


 * I got it, but it is too large to type in. :-) Bubba73 You talkin' to me? 03:41, 1 April 2019 (UTC)


 * According to this article, this is an unsolved problem. The corresponding problem for 33 instead of 42 has just been solved and involves 16-digit numbers. --76.69.46.228 (talk) 05:44, 1 April 2019 (UTC)
 * There is a Numberphile video on this as well. Happy April 1 folks! --RDBury (talk) 09:33, 1 April 2019 (UTC)

Compounding & smoothed values
Hi, I have a maths problem which I can't figure out how to resolve, though it might be fairly simple to the users on here.

I have a set of values which increase by 125% every 25 days. As follows:

and so on...

This is all the information we have, and that the data would follow a smoothed upward trajectory. My question is how I predict a value which is not a multiple of 25. For example how do I predict what the value would be on day 120, according to the pattern of this data? Uhooep (talk) 10:17, 1 April 2019 (UTC)
 * The formula for exponential growth is $$x_t = x_0(1+r)^t$$ = 50×(1 + 125%)day/25 = 50×2.25day/25. After 120 days it is  = . PrimeHunter (talk) 10:52, 1 April 2019 (UTC)

I wonder who was the first to discover the well known formula of the Sine (or the Cosine or the Tangent) of sum of angles.
HOTmag (talk) 12:56, 1 April 2019 (UTC)


 * See History of trigonometry. --JBL (talk) 14:03, 1 April 2019 (UTC)
 * Thx. HOTmag (talk) 13:20, 2 April 2019 (UTC)