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Show that any positive integer is of the form 6q+1,6q+3,6q+5where q is some integer |
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Answer» We Consider An positive integer as a.On dividing a by b .Here , let q is the quotient and r is the remainder.Now, a = bq + r , 0 ≤ r < b ..... ( 1 )[ by using Euclid\'s division lemma]Here we putting b = 6 in eq ( 1 )Here we find , a = 6q + r , 0 ≤ r < b ..... ( 2 )so here possible values of r = 1 , 2, 3, 4, 5.If r = 0, then find Equation (2) , a = 6q.Here, 6q is is divisible by 2 , so 6q is here Even .If r = 1 , then find Equation (2) , a = 6q + 1.Here, 6q + 1 is not divisible by 2 , so 6q + 1 is here odd.If r = 2 , then find Equation (2) , a = 6q + 2.Here, 6q + 2 is not divisible by 2 , so 6q + 2 is here even.If r = 3 , then find Equation (2) , a = 6q + 3.Here, 6q + 3 is not divisible by 2 , so 6q + 3 is here odd.If r = 4 , then find Equation (2) , a = 6q + 4.Here, 6q + 4 is not divisible by 2 , so 6q + 4 is here even.If r = 5 , then find Equation (2) , a = 6q + 5.Here, 6q + 5 is not divisible by 2 , so 6q + 5 is here odd.so , a is odd , so a cannot be 6q,6q+2, 6q+4.Therefore any positive odd integer is of the form 6q+1 , 6q +3, 6q + 5. Aese kyun bol rahe ho, deepak to sirf question puche hein, ye kaise answer hota hai |
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