Bad Fraction Reduction That Actually Works1664=14This is certainly not a correct technique for reducing fractions to lowest terms, but it happens to work in this case, and I believe there are other such examples. Is there a systematic way to generate examples of this kind of bad fraction reduction?

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zakulisan337 · Accepted Answer

It&#039;s easy to find them all. Suppose 10a+n10n+b=ab. Thus  (10a−b)n=9ab.Case 1:(9,n)=1:9 | 10:a−b ⇒ 9 | a−b ⇒a=b ⇒ 9:a:n=9:a2 ⇒ n=a=b(trivial)Case 2:(9,n)=9:: 10:a−b=a:b ⇒ a∣b, 10=(ba):(a+1) so a,b=1,5  or  4,8 which yields the solutions: 1995=15 and 4998=12. Similar analysis of the remainingCase 3: (9,n)=3: yields 1664=14, and 2665=25.

Bad Fraction Reduction That Actually Works \(\displaystyle{\frac{{{16}}}{{{64}}}}={\frac{{{1}}}{{{4}}}}\) This is

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