Divisibility
Divisibility is whether one integer divides another with no remainder, the foundation of number theory.
At a glance
Key signals
0% cross fields · reaches 1 more
- Number Theory
- Mathematics
- Explanation
- Examples
- Misconception
- Sourced relations
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Enables · leads to
Fundamental theorem of arithmeticdepends onDivisibilityEstablished
Open Fundamental theorem of arithmetic →
The fundamental theorem of arithmetic is a statement about divisibility by primes.
Mechanism: It asserts every integer greater than one factors uniquely into primes — the primes being exactly the numbers with no non-trivial divisors.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 3 of 3 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Structural neighbourhood: 3 → 9 → 18 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 3 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
3 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
What builds on this
1 concept build on this directly, 1 in total, across 2 disciplines.
Structural downstream reach along dependency edges — not a claim of historical necessity.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Modular arithmetic and Fundamental theorem of arithmetic.
Through this lens it connects to Integer, Modular arithmetic and Fundamental theorem of arithmetic.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
- Connects 3 other ideas across 2 disciplines.
- Most of its connections are of the “Teaching link” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
- Divisibility verified
- More on divisibility verified