euclid division lemma to show that cube of any positive integer9m,9m+1or9m+8
Answers
✺[н̲̲̅̅σ̲̲̅̅l̲̲̅̅α̲̲̅̅ ̲̲̅̅υ̲̲̅̅s̲̲̅̅є̲̲̅̅я̲̲̅̅s̲̅]✺
⊰᯽⊱┈──╌❊╌──┈⊰᯽⊱
✪☙[н̲̲̅̅є̲̲̅̅y̲̲̅̅ ̲̲̅̅м̲̲̅̅α̲̲̅̅т̲̲̅̅є̲̲̅̅ ̲̲̅̅н̲̲̅̅є̲̲̅̅я̲̲̅̅є̲̲̅̅ ̲̲̅̅i̲̲̅̅s̲̲̅̅ ̲̲̅̅y̲̲̅̅σ̲̲̅̅υ̲̲̅̅я̲̲̅̅ ̲̲̅̅α̲̲̅̅и̲̲̅̅s̲̲̅̅w̲̲̅̅є̲̲̅̅я̲̲̅̅:̲̲̅̅-̲̅]☙✪
══════ •『 ♡ 』• ══════
☞Let a be any positive integer and b = 3
a = 3q + r, where q ≥ 0 and 0 ≤ r < 3
☙☙☙☙☙☙☙☙☙☙
Therefore, 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) 3
a 3 = 27q 3 + 27q 2 + 9q + 1
a 3 = 9(3q 3 + 3q 2 + q) + 1
a 3 = 9m + 1
Where m is an integer such that m = (3q 3 + 3q 2 + q)
Case 3: When a = 3q + 2,
a 3 = (3q +2) 3
a 3 = 27q 3 + 54q 2 + 36q + 8
a 3 = 9(3q 3 + 6q 2 + 4q) + 8
a 3 = 9m + 8
Where 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.☙☙☙
❛ ━━━━━━･❪ ❁ ❫ ･━━━━━━ ❜
☞ ♥•♥•♥•♥•♥•✺Hope it helps bro.. ❁❢◥ ▬▬▬▬▬ ◆ ▬▬▬▬▬ ◤❢