<prompt> Ikiwa a, b, x, na y ni nambari halisi kama vile axby3, ax2by27, ax3by3 16, na ax4by442, pata ax5by5.  <response>: Kwa n 1, 2, 3, 4, 5, define s_n axn byn. Tumepewa thamani za s_1, s_2, s_3, na s_4, na tunataka hesabu s_5.Tunapata uhusiano kati ya masharti s_n. Ona kwamba beginaligned xyaxn byn axn1 bxyn ax ny kwan1 shokan1 kwan1 xyshokan-1 kwan-1. endalignedKwa maneno mengine, xy s_n s_n1 xys_n-1 kwa n. zote Kwa hivyo, kuchukua n2 na n 3, tunapata beginaligned 7xy 16 3xy 16xy 42 7xy. mwishozilizowianishwaKutatua mfumo huu wa milinganyo kwa xy na xy kunatoa xy -14 na x-38. Hivyo, tukichukua n4, tunapata 42xy s_5 16xy,hivyo s_5 42-14 - 16-38 20. 