<prompt> Ni nakala ngapi nne tofauti a, b, c, d za nambari mantiki ziko naa cdot logi_10 2b cdot logi_10 3 c cdot log_10 5 d cdot log_10 7 2005?  <response>: Tunaweza kuandika equation iliyotolewa kamalogi_10 2a logi_10 3b logi_10 5c logi_10 7d 2005.Kishalogi_10 2a cdot 3b cdot 5c cdot 7d 2005,hivyo 2a cdot 3b cdot 5c cdot 7 d 102005.Kwa kuwa a,b, c, d zote ni za busara, kuna nambari kamili chanya M ili aM, bM, cM, dM zote ni nambari kamili. Kisha2aM cdot 3bM cdot 5cM cdot 7dM 102005M 22005M cdot 52005M. Kutoka kwa uainishaji wa kipekee, lazima tuwe na aM 2005M, bM 0, cM 2005M, na dM 0. Kisha a 2005, b 0, c 2005, na d 0. Hivyo, kuna 1 tu mara nne, yaani a,b,c,d 2005,0,2005,0. 