MathDB
Uniqueness question

Source: Tournament of Towns,Spring 2002, Junior O Level, P1

May 13, 2014
geometryrectanglenumber theorygreatest common divisorcombinatorics proposedcombinatorics

Problem Statement

There are many a×ba\times b rectangular cardboard pieces (a,b∈Na,b\in\mathbb{N} such that a<ba<b). It is given that by putting such pieces together without overlapping one can make 49×5149\times 51 rectangle, and 99×10199\times 101 rectangle. Can one uniquely determine a,ba,b from this?
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