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Tag: Bmo1 Number Theory
All BMO and UKMT Pathway Guide editorial articles matching this filter. Browse the full archive at News & Updates, or use the navigation to filter by stage, paper, or topic tag.
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BMO1 Diophantine equations: factor or bound? A decision table for two-variable proofs
BMO1 Diophantine equations need a structural decision: factor a product form or bound a variable. This guide gives a decision table, a complete positive-integer factor-pair audit, and a finite-range bound check. Read article
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BMO Infinite Descent: How to Write a Complete Proof
A guide to completing BMO-style infinite descent proofs by choosing a least positive solution, preserving integrality, and proving strict decrease. Read article
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The BMO1 Number Theory and Combinatorics Toolkit: Parity, Invariants, Pigeonhole and the Right Modulus
Parity, invariants, pigeonhole and choosing the right modulus: how to make BMO1 number theory and combinatorics systematic instead of a matter of luck. Read article