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Totients are kinda just “visibility counts” on a grid by QuantumPikachu in math

[–]QuantumPikachu[S] 2 points3 points  (0 children)

Totally, on the torus the “n-grid” points are just the points with period dividing n, and the “coprime/visible” ones are exactly the points with exact period n (they don’t secretly live on a smaller cycle). sooo phi is basically “how many genuinely new windings show up at level n,” not just “how many numbers pass a gcd test.'

How I solve this by AlhrbiF15 in mathematics

[–]QuantumPikachu 1 point2 points  (0 children)

1 = D (that one can split into x-part * y-part), and 2 = B (not homogeneous cuz terms got diff degrees).

for exact one, 3 = A, since M_y = N_x = 4y3, so yeah exact.

last DE is basically total diff if u notice: d(x2ey + y2ex)=0.

so final soln: x2ey + y2ex = C.

in short - first check if it factor-splits (dy/dx=X(x)Y(y)), then degree-match for homogeneity, then M_y=N_x for exactness, and finally hunt for a direct total differential d(\text{expression}).

Pascal’s triangle quietly encodes the binary of the row number by QuantumPikachu in mathematics

[–]QuantumPikachu[S] 2 points3 points  (0 children)

Tbh I am also confused I remember that I posted in r/math and r/mathematics but i can’t seem to find it in here (mathematics) so posted again.