#math trivia #238 solution

The other numbers are:

  • 101, 111, 121, 131, 141, 151, 161, 171, 181, 191
  • 201, 212, 224 (next would be the current 238)
  • 301, 313, 329
  • 401, 414
  • 501, 515
  • 601, 616
  • 701, 717
  • 801, 818
  • 901, 919

The ones that may not be so obvious are the ones with b = 0.   But recall that the 0th power of every number is 1.  This makes the exponentiation law work out:  x(y+z) = xy * xz.  If z = 0, then x(y+z) = xy, which requires that xz be 1.

Other trivia:  Most of these numbers could be US area codes — which ones couldn’t?  And many could be route numbers of US Interstate highways — again, which ones couldn’t?  Notably, 238 itself is one of the anomalies in the Internet highway numbering system, more than a trivial concern to highway buffs.

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