Clock Arithmetic & Modular Explorer

Analog Clock Dial (ℤ_6) Pointer: 1

Hand / Remainder (r)

Wrap Trail

Starting Base

Full Wraps (q)

Modulus m (2 to 36): 6

Arithmetic Parameters & Proof x = q × m + r

Quora Discussion Presets:

Base Integer (x)

Modulus (m)

Add/Subtract Offset (Δ)

Source Expression: x = 7, m = 6

Canonical Equation: 7 = 1 mod 6 (7 = 1 + (1)(6))

Clock Dial Position (r ∈ ℤ_m): 1

Full Laps / Quotient (q): 2

Remainder after offset (R): 1

Modular Inverse of (x mod m) in ℤ_m: N/A (gcd != 1)

Coprime Status: gcd(x, m) = 1

Evaluating: 7 mod 6 → Hand starts at 0, wraps clockwise 1 full lap (6 units), lands at position 1. Adding offset 6 → total 13 = 2 full laps + remainder 1.

Activity & Evaluation Log:

Init: x=7, m=6, offset=6Pos: 1