## Ingenuity in mathematics |

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AABC abundant numbers Allen Shields angle arithmetic arithmetic progression assertion Barbier's theorem Beatty sequences C. D. Olds centre circle circumference common factor congruent consecutive construct curve denote difference digits divisible divisors equal equation ESSAY example Exercise Farey Sequence Farey Series Figure follows formula fractions geometric given gives H. S. M. Coxeter Hence inequality interior lattice points intersection interval Lemma length Mathematics move multiples non-square number of positive obtain occur odd number parallel partial sums partition perfect number perfect square perimeter of pn perpendicular Pick's Theorem polygon positive integer prime numbers primitive triangles problem Proof prove Pythagorean triples radius rectangle relatively prime result Reuleaux triangle satisfy segment sequence sides simple polygon smallest solution statement straight line straightedge Suppose theorem triangle ABC vertex vertices visible point winning positions yields zero