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Show that any positive odd integer is of the form 6q+1, or 69 +3, or 6q +5, where q issome integer. |
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Answer» Answer: The below is ur answer Step-by-step EXPLANATION: Let a be any positive INTEGER and B = 6. Then, by Euclid’s algorithm, a = 6Q + r, where 0≤r<6 , r = 0, 1, 2, 3, 4, 5 If r = 0, a = 6q + r = 6q + 0 = 6q = 2 * 3q If r = 1, a = 6q + 1 If r = 2, a = 6q + 2 = 2 ( 3q + 1) If r = 3, a = 6q + 3 =3 ( 2q + 1 ) If r = 4, a = 6q + 4 =2 (3q + 2) If r = 5, a = 6q + 5 2 is factor of all positive integers 6q , 6q + 2 , 6q + 4 are even numbers Hence 6q + 1 , 6q + 3 and 6q + 5 are positive odd integers |
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