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

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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:

Number of days	Value
Day 0	50
Day 25	112.5
Day 50	253.125
Day 75	569.53125
Day 100	1281.445313
Day 125	2883.251953

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)

Template:Ping The formula for exponential growth is $x_t=x_0(1+r{)}^t$ = 50×(1 + 125%)^day/25 = 50×2.25^day/25. After 120 days it is {{#expr:50*2.25^(120/25)}} = 2451.5801216619. 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)