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 A Really Weird Math Problem (Posted on 2018-03-12)
On The Big Bang Theory's episode "The Athenaeum Allocation", Sheldon mentions to Amy that for their proposed wedding date, May 12,

"The month squared equals the square of the sum of the members of the set of the prime factors of the day. Isn't that romantic?"

Amy's reply contorts a Shakespeare quote: "shall I compare thee to a day that's also a really weird math problem?"

It's indeed weird as the squaring is introduced for no reason at all.

But also, how rare is the circumstance? What other dates of the year exhibit the property? Remember that because of the set-membership criterion, each prime factor is included in the sum only once: 12 has prime factors 2 and 3, and those add up to 5, for May.

 See The Solution Submitted by Charlie No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Spoiler (I think . . .) | Comment 2 of 4 |
There are quite a few good candidates.
Let D = day, M = month, PF_i = i-th prime factor of D (i = 1, ..., n)
Then,           M = sigma {i=1,... n} PF_i

D    PF    M   Good Date
2     2      2     Feb 2
3     3      3     Mar 3
4     2      2     Feb 4
5     5      5     May 5
6    2, 3   5     May 6
7     7      7     Jul 7
8     2      2     Feb 8
9     3      3     Mar 9
10   2, 5    7    Jul 10
11    11   11    Nov 11
12   2, 3    5     May 12
14   2, 7    9     Sep 14
15   3, 5    8     Aug 18
16     2      2     Feb 16
18   2, 3    5     May 18
20   2, 5    7     Jul 20
21   3, 7   10    Oct 21
24   2, 3     5     May 24
25     5       5     May 25
27     3       3      Mar 27
28    2,  7   9      Sep 28
30  2, 3, 5   10    Oct 10

In summary:  Jan (none except the trivial Jan 1)
Feb 2, 4, 8, 16
Mar 3, 9, 27
Apr   (none)
May 5, 6, 12, 18, 24, 25
Jun   (none)
Jul  7, 10, 20
Aug 8
Sep 14, 28
Oct 10, 21
Nov 11
Dec  (none)
Thanks BBT and Charlie!

 Posted by JayDeeKay on 2018-03-12 11:56:10

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