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IOQM 2018Integers a, b, c satisfya+b−c=1anda2+b2−c2=−1.What is the sum of all possible values ofa2

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IOQM 2018Let ABCD be a trapezium in which AB∥CD and AD⊥AB. Suppose ABCD has an incircle which touche

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IOQM 20184. The equation 166×56=8590 is valid in some base b≥10 (that is, 1,6,5,8,9, and 0 are

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IOQM 2018Consider all 6-digit numbers of the form abccba, where b is odd. Determine the number of

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IOQM 2018quadrilateral ABCD with AB = AD = 13, BC = CD = 20, and BD = 24.

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IOQM 2018A book is published in three volumes, the pages being numbered from 1 onwards. The page nu

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n→∞lim (n4+1 n −(n2+1)n4+1 2n +n4+16 n −(n2+4)n4+16 8n +⋯+n4+n4 n −(n2+n2)n4+n4 2n⋅n2 .

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Let [t] denote the greatest integer less than or equal to t. Then the least value of p∈N for which

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