Some notes

Some notes:

(N+X) mod (N-X) = (2*N) mod (N-X)

for 2< X < N ... but why?

Because: (2*N) / (N-X) = (N+X)/(N-X) + (N-X)/(N-X) = (N+X+N-X)/(N-X)

also:

(N+2*X) mod (N-X) = (3*N) mod (N-X)

and also: (N-X)-((N-3*X) mod (N-X)) = (2*N) mod (N-X)

General rule

(N+V*X) mod (N-X) = ((V+1)*N) mod (N-X)

(N+V*X) mod (N-X) = (V*N+N) mod (N-X)

(N-X)-((N-(V+1)*X) mod (N-X)) = (V*N) mod (N-X)

for V ∈ N, N ∈ N, X ∈ N.

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(N-1)!+1 = A * N

for A ∈ N, N ∈ N.

(also maybe: (N-2)!-1 = A * N ; still need to figure out why)

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(where [ and ] stands for "floor")

Reminder to myself

Need to improve sketch_190223b to visualize negative numbers.

Those seem to have an important impact ...

Created a primitive image just in case i can't remember later

Wolframalpha research

#1

#2

• (some weird involvement with pi)
• • but: since floor is used in #1, this may not play any role at all

#1 & #2

#3

#4

#5

#6_1 #6_2

#7 cos(π/p) = -cos((π Γ(p))/p)

#8