Mathematics Homework Solutions
#27709
Proof about congruence modulo 43 (also expressible as equivalence modulo 43)
Let S = Z_43 (where the underscore, "_", indicates that what follows it, in this case 43, is a subscript). Let Q be a subset of S that contains ten non-zero numbers (i.e., that Q contains ten non-zero elements of S). Prove that Q contains four distinct numbers "a," "b," "c," "d" such that ab = cd in Z_43.
A detailed, step-by-step proof (of the statement that Q contains four distinct numbers "a," "b," "c," "d" such that ab = cd in Z_43) is provided.
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