<prompt> Tafuta nambari kamili n kiasi kwamba 1leftfloordfrac101rightfloorleftlceildfrac99n100rightrceil.  <response>: Hebufn leftlceil frac99n100 kuliarceil - leftfloor frac101 rightfloor.Kumbuka kwambaanzaalignfn 10100 kushotolceil frac99 n 10100100 kuliarceil - leftfloor frac100 n 10100101 kulia sakafu kushotolceil frac99n100 101 kuliarceil - leftfloor frac101 100 kuliasakafu kushotolceil frac99n100 kuliarceil 101 - leftfloor frac100n101 kuliasakafu - 100 kushotolceil frac99n100 kuliarceil - leftfloor frac101 kuliasakafu 1 fn 1.endalignHii inamaanisha kwamba kwa kila darasa la masalio r modulo 10100, kuna nambari kamili ya kipekee n kiasi kwamba fn 1 na n equiv r pmod10100. Hivyo, jibu ni 10100. 