1५५७४ A SIS Ml Ber. Oice,y T VR, R sen3 nae. AL whial s o aion A,Q) 2 15 VE. z\m\eﬂw A wY AV लक MM_%%‘MJ

1५५७४ A SIS Ml Ber. Oice,y T VR, R sen3 nae. AL whial s o aion

1.	1५५७४ A SIS Ml Ber. Oice,y T VR, R sen3 nae. AL whial s o aion A,Q) 2 15 VE. z\m\eﬂw A wY AV लक MM_%%‘MJ
Answer» Let a be any positive integer and b = 3a = 3q + r, where q ≥ 0 and 0 ≤ r < 3Therefore, every number can be represented as these three forms. There are three cases.Case 1: When a = 3q,Where m is an integer such that m = Case 2: When a = 3q + 1,a^3= (3q +1)^3a^3= 27q^3+ 27q^2+ 9q + 1a^3= 9(3q^3+ 3q^2+ q) + 1a^3= 9m + 1Where m is an integer such that m = (3q^3+ 3q^2+ q)Case 3: When a = 3q + 2,a^3= (3q +2)^3a^3= 27q^3+ 54q^2+ 36q + 8a^3= 9(3q^3+ 6q^2+ 4q) + 8a3= 9m + 8Where m is an integer such that m = (3q^3+ 6q^2+ 4q)Therefore, the cube of any positive integer is of the form 9m, 9m + 1, or 9m+8