a and b for which a b = a . b ¯ Are there natural numbers a and b such that a b = a . b ¯ ?I know that a . b ¯ = a + ∑ i = 1 n b i 10 − i where b i is the ith digit of b and b has n digits.I also know that b = ∑ i = 1 n b i 10 n − i

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a and   b for which       a    b    =            a      .      b        ¯  Are there natural numbers   a and   b such that       a    b    =            a      .      b        ¯  ?I know that             a      .      b        ¯    =  a  +      ∑          i      =      1              n            b    i        10          −      i       where       b    i   is the   ith digit of   b and   b has   n digits.I also know that   b  =      ∑          i      =      1              n            b    i        10          n      −      i

Tianna Deleon · Accepted Answer

So,       10    n    ×            a      .      b        ¯    =  a  ×      10    n    +  b, yes? Meaning that you want       10    n    ×      a    b    =  a  ×      10    n    +  b. But this implies that  a  ×      10    n    ×      (    1    −          1      b        )    +  b  =  0But this is impossible, given that   b  ≥  1

a and b for which a b </mfrac> = <mover> a . b

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