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Find all fractions which satisfy the property

Source: IMO LongList 1979 - P34

June 3, 2011
SFFTnumber theory proposednumber theory

Problem Statement

Notice that in the fraction 1664\frac{16}{64} we can perform a simplification as 1664=14\cancel{\frac{16}{64}}=\frac 14 obtaining a correct equality. Find all fractions whose numerators and denominators are two-digit positive integers for which such a simplification is correct.
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