Wikipedia:Reference desk/Archives/Mathematics/2017 May 6

= May 6 =

Kaprekar numbers
Are Kaprekar numbers idempotent under multiplication modulo 1 less than the next higher power of 10? GeoffreyT2000 (talk) 17:56, 6 May 2017 (UTC)
 * Apparently, 4879 is a counterexample. It is Kaprekar because $$4879^2=23804641$$ and $$238+04641=4879$$, but $$4879^2\equiv7021\mod 9999$$.
 * Clearly this happens because the split of 23804641 happens at the "wrong" location. I suspect the property should be easily provable for numbers which are Kaprekar by splitting at the middle. -- Meni Rosenfeld (talk) 19:13, 6 May 2017 (UTC)
 * Among the (base-10) Kaprekar numbers listed in the article, the exceptions are 4879, 5292 and 38962. -- Meni Rosenfeld (talk) 19:19, 6 May 2017 (UTC)