Re:Euler's Fizzbuzz (2020)
by svat on Wednesday March 17, 2021 @12:25PM
(#26493356)
Ah, clicking the footnote numbers worked for footnotes 1 to 4, but not for 5 and 6.
BTW, for the question “Where do the constant values 0, 6, 10, and 1 come from?”, though it's implicit in the post, it is useful to note explicitly that as x^4 takes only the values 0 or 1 either mod 3 or mod 5, these four possibilities—namely (0,0), (0,1), (1,0), (1,1)—precisely account for those values:
(0 mod 3) and (0 mod 5) ⇔ (0 mod 15)
(0 mod 3) and (1 mod 5) ⇔ (6 mod 15)
(1 mod 3) and (0 mod 5) ⇔ (10 mod 15)
(1 mod 3) and (1 mod 5) ⇔ (1 mod 15)
This would also simplify the post considerably maybe, as much of the algebra wouldn't be needed.
BTW, for the question “Where do the constant values 0, 6, 10, and 1 come from?”, though it's implicit in the post, it is useful to note explicitly that as x^4 takes only the values 0 or 1 either mod 3 or mod 5, these four possibilities—namely (0,0), (0,1), (1,0), (1,1)—precisely account for those values:
This would also simplify the post considerably maybe, as much of the algebra wouldn't be needed.